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• 1. Basic Concepts
• 2. Classical Analytical Methods of Optimization
• 3. Numerical Search Methods for Unconstrained Optimization Problems
• 4. Stochastic and Evolutionary Optimization Algorithms
• 5. Application of Stochastic and Evolutionary Optimization Algorithms to Base Case Problems
• 6. Applications to Chemical Processes
• 7. Applications to Biochemical Processes
• 8. Applications to Pharmaceutical Processes
• 9. Applications to Environmental Processes
• 10. Conclusions.
• (source: Nielsen Book Data)

Stochastic global optimization methods and applications to chemical, biochemical, pharmaceutical and environmental processes presents various algorithms that include the genetic algorithm, simulated annealing, differential evolution, ant colony optimization, tabu search, particle swarm optimization, artificial bee colony optimization, and cuckoo search algorithm. The design and analysis of these algorithms is studied by applying them to solve various base case and complex optimization problems concerning chemical, biochemical, pharmaceutical, and environmental engineering processes. Design and implementation of various classical and advanced optimization strategies to solve a wide variety of optimization problems makes this book beneficial to graduate students, researchers, and practicing engineers working in multiple domains. This book mainly focuses on stochastic, evolutionary, and artificial intelligence optimization algorithms with a special emphasis on their design, analysis, and implementation to solve complex optimization problems and includes a number of real applications concerning chemical, biochemical, pharmaceutical, and environmental engineering processes.
(source: Nielsen Book Data)

The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramer-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.
(source: Nielsen Book Data)

• Combinatorial Analysis.- Basic Concepts in Probability.- Conditional Probability, Bayes's Formula, Independent Events.- Introduction to Random Variables.- Discrete Random Variables.- Continuous Random Variables.- Other Selected Topics in Basic Probability.- A Brief Introduction to Stochastic Processes.- A Brief Introduction to Point Process, Counting Process, Renewal Process, Regenerative Process, Poisson Process.- Poisson Process.- Renewal Process.- An Introduction to Markov Chains.- Special Discrete-Time Markov Chains.- Continuous-Time Markov Chains.- An Introduction to Queueing Models.- Introduction to Brownian Motion.- Basics of Martingales.- Basics of Reliability Theory.
• (source: Nielsen Book Data)

This textbook explores probability and stochastic processes at a level that does not require any prior knowledge except basic calculus. It presents the fundamental concepts in a step-by-step manner, and offers remarks and warnings for deeper insights. The chapters include basic examples, which are revisited as the new concepts are introduced. To aid learning, figures and diagrams are used to help readers grasp the concepts, and the solutions to the exercises and problems. Further, a table format is also used where relevant for better comparison of the ideas and formulae. The first part of the book introduces readers to the essentials of probability, including combinatorial analysis, conditional probability, and discrete and continuous random variable. The second part then covers fundamental stochastic processes, including point, counting, renewal and regenerative processes, the Poisson process, Markov chains, queuing models and reliability theory. Primarily intended for undergraduate engineering students, it is also useful for graduate-level students wanting to refresh their knowledge of the basics of probability and stochastic processes.
(source: Nielsen Book Data)

• Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; List of Tables; Preface;
• Chapter 1 Stochastic Processes, Markov Chains and Continuous-Time Applications; 1.1. Introduction; 1.2. Preliminary Results;
• Chapter 2 Poisson Processes; 2.1. Punctual Processes; 2.2. Poisson Processes Definition; 2.3. Definition Form of a Point Process; 2.4. Properties; 2.5. Main Results; 2.6. Determining The Ordering; 2.7. Alternative Definitions of Poisson Processes; 2.8. Poisson Processes In Two or More Dimensions; 2.9. Projections; 2.10. Poisson Process

• 2.11. Processes Which Are Not Homogenous
• Chapter 3 Markov Chains In Continuous Time; 3.1. Pure Markov Processes; 3.2 Properties; 3.3. Explosions; 3.4 Kolmogorov Equations; 3.5. Classification of States And Invariant Measures; 3.6. Skeleton Process; 3.7. Birth And Death Processes;
• Chapter 4 Applications In Biology; 4.1. Modeling The Growing Populations;
• Chapter 5 Network Analysis Modeled With Stochastic Processes; 5.1. Introduction; 5.2. Statement of The Problem; 5.3. Justification of Using Stochastic Processes; 5.4. The Objectives; 5.5. Theoretical Framework; 5.6. Time Series Models

• 5.7. Stochastic Processes5.8. Entropy as a Measure of Information; 5.9. Markov Chains In Continuous Time: Liability of a Multiprocessor; 5.10. Queuing; 5.11. Queue Networks; 5.12. Experiment Design; 5.13. Simulation Experiment; 5.14. Experimental Results; 5.15. General Analysis System; 5.16. Design of The Optimization Model; 5.17. Optimization Model; 5.18. Model Solution; 5.19. Tool Design;
• Chapter 6 Stochastic Modeling And Simulation; 6.1. Counting Processes; 6.2. Theory of Tails; 6.3. Variations Model M/G/1; Appendixs; Conclusions; Bibliography; Index

Random processes are one of the most powerful tools in the study and understanding of countless phenomena in natural and social sciences. The book is a complete medium-level introduction to the subject. The book is written in a clear and pedagogical manner but with enough rigor and scope that can appeal to both students and researchers. This book is addressed to advanced students and professional researchers in many branches of science where level crossings and extremes appear but with some particular emphasis on some applications in socio-economic systems.
(source: Nielsen Book Data)

• 0. Preface.- List of contributors.-
• 1. Youri Davydov, Valentin Konakov, Roberto Garra and Enzo Orsingher: Random motions.-
• 2. Aurelien Alfonsi, Masafumi Hayashi, Arturo Kohatsu-Higa, Gennaro Cibelli and Sergio Polidoro: Parametrix and heat kernel estimates.-
• 3. Ion Grama and Emile Le Page: Local limit theorems.-
• 4. Denis Belomestny, Stefan Hafner, Mikhail Urusov, Alexander Gushchin and Esko Valkeila: Approximation of stochastic processes.-
• 5. Alexandre Richard, Denis Talay, Yuliya Mishura and Kostiantyn Ralchenko: Fractional Brownian motion.-
• 6. Alexander Lykov, Vadim Malyshev, Bernard Derrida and Zhan Shi: Particle systems.-
• 7. Pierre Bellec, Alexandre Tsybakov and Enno Mammen: Statistics.-
• 8. Ekaterina Bulinskaya: Acturial science.-
• 9. Dan Han, Stanislav Molchanov, Joseph Whitmeyer: Population dynamics.-
• 10. Alexander Veretennikov: Ergodic Markov processes.
• (source: Nielsen Book Data)

This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference "Modern problems of stochastic analysis and statistics", held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.
(source: Nielsen Book Data)

• Preliminaries.- Minimality, Rigidity, and Flows.- Mixed Moving Averages and Self-similarity.- A. Historical Notes.- B. Standard Lebesgue Spaces and Projections.- C. Notation Summary.
• (source: Nielsen Book Data)

This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
(source: Nielsen Book Data)

• Preface.- Notations.- Basic facts.- Stochastic calculus.- Distributions of functionals of Brownian motion.- Diffusion processes.- Brownian local time.- Diffusions with jumps.- Invariance principle for random walks and local times.-
• Appendix 1. Heat transfer problem.-
• Appendix 2. Special functions.-
• Appendix 3. Inverse Laplace transforms.-
• Appendix 4. Differential equations and their solutions.-
• Appendix 5. Examples of transformations of measures associated with diffusion processes.-
• Appendix 6. Formulae for n-fold differentiation.- Bibliography.- Subject index.
• (source: Nielsen Book Data)

This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times.Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
(source: Nielsen Book Data)

• Avant-propos
• Pile, face, coupons
• Marches aléatoires
• Branchement et processus de Galton-Watson
• Permutations, partitions, et graphes
• Mesures de Gibbs
• Agrégation limitée par diffusion interne
• Chaînes de Markov cachées
• Chaînes de Markov cachées
• Algorithme EM et mélanges
• Urnes d'Ehrenfest
• Records, extrêmes, et recrutements
• File d'attente M/M/Infini
• Modèle de Wright-Fisher
• Généalogies et coalescence
• Restaurants chinois
• Renforcement
• Percolation
• Croissance et fragmentation
• Ruine d'une compagnie d'assurance
• Polymères dirigés en environnement aléatoire
• Problème du voyageur de commerce
• Matrices aléatoires
• Naissances et assassinats
• Modèle du télégraphe
• Problème de Dirichlet
• Processus d'Ornstein-Uhlenbeck
• Modèles de diffusion cinétique
• Des chaînes de Markov aux processus de diffusion
• Suggestions bibliographiques
• Littérature
• Index
• Principales notations et abréviations.

Ce recueil puise sa source dans les cours de master de mathématiques appliquées et de préparation à l'épreuve de modélisation de l'agrégation de mathématiques. Le parti pris de cet ouvrage est de polariser la rédaction par les modèles plutôt que par les outils, et de consacrer chaque chapitre à un modèle. Le premier public visé est celui des enseignants-chercheurs en probabilités, débutants ou confirmés. De nombreux chapitres peuvent également bénéficier directement à des étudiants de master ou préparant l'agrégation. Collected Stochastic Models This collection was inspired by applied mathematics Master classes in stochastic modeling. The focus is on models rather than on tools, and each chapter is devoted to a specific model. Though the book is primarily intended for academics in the field of probability theory, beginners and experienced researchers alike, many chapters will also benefit students preparing to pursue their Master degree in mathematics. .

• INTRODUCTION xi
• CHAPTER 1. BASIC PROBABILISTIC TOOLS FOR STOCHASTIC MODELING 1
• 1.1. Probability space and random variables 1
• 1.2. Expectation and independence 4
• 1.3. Main distribution probabilities 7
• 1.3.1. Binomial distribution 7
• 1.3.2. Negative exponential distribution 8
• 1.3.3. Normal (or Laplace Gauss) distribution 8
• 1.3.4. Poisson distribution 11
• 1.3.5. Lognormal distribution 11
• 1.3.6. Gamma distribution 12
• 1.3.7. Pareto distribution 13
• 1.3.8. Uniform distribution 16
• 1.3.9. Gumbel distribution 16
• 1.3.10. Weibull distribution 16
• 1.3.11. Multi-dimensional normal distribution 17
• 1.3.12. Extreme value distribution 19
• 1.4. The normal power (NP) approximation 28
• 1.5. Conditioning 31
• 1.6. Stochastic processes 39
• 1.7. Martingales 43
• CHAPTER 2. HOMOGENEOUS AND NON-HOMOGENEOUS RENEWAL MODELS 47
• 2.1. Introduction 47
• 2.2. Continuous time non-homogeneous convolutions 49
• 2.2.1. Non-homogeneous convolution product 49
• 2.3. Homogeneous and non-homogeneous renewal processes 53
• 2.4. Counting processes and renewal functions 56
• 2.5. Asymptotical results in the homogeneous case 61
• 2.6. Recurrence times in the homogeneous case 63
• 2.7. Particular case: the Poisson process 66
• 2.7.1. Homogeneous case 66
• 2.7.2. Non-homogeneous case 68
• 2.8. Homogeneous alternating renewal processes 69
• 2.9. Solution of non-homogeneous discrete timevevolution equation 71
• 2.9.1. General method 71
• 2.9.2. Some particular formulas 73
• 2.9.3. Relations between discrete time and continuous time renewal equations 74
• CHAPTER 3. MARKOV CHAINS 77
• 3.1. Definitions 77
• 3.2. Homogeneous case 78
• 3.2.1. Basic definitions 78
• 3.2.2. Markov chain state classification 81
• 3.2.3. Computation of absorption probabilities 87
• 3.2.4. Asymptotic behavior 88
• 3.2.5. Example: a management problem in an insurance company 93
• 3.3. Non-homogeneous Markov chains 95
• 3.3.1. Definitions 95
• 3.3.2. Asymptotical results 98
• 3.4. Markov reward processes 99
• 3.4.1. Classification and notation 99
• 3.5. Discrete time Markov reward processes (DTMRWPs) 102
• 3.5.1. Undiscounted case 102
• 3.5.2. Discounted case 105
• 3.6. General algorithms for the DTMRWP 111
• 3.6.1. Homogeneous MRWP 112
• 3.6.2. Non-homogeneous MRWP 112
• CHAPTER 4. HOMOGENEOUS AND NON-HOMOGENEOUS SEMI-MARKOV MODELS 113
• 4.1. Continuous time semi-Markov processes 113
• 4.2. The embedded Markov chain 117
• 4.3. The counting processes and the associated semi-Markov process 118
• 4.4. Initial backward recurrence times 120
• 4.5. Particular cases of MRP 122
• 4.5.1. Renewal processes and Markov chains 122
• 4.5.2. MRP of zero-order (PYKE (1962)) 122
• 4.5.3. Continuous Markov processes 124
• 4.6. Examples 124
• 4.7. Discrete time homogeneous and non-homogeneous semi-Markov processes 127
• 4.8. Semi-Markov backward processes in discrete time 129
• 4.8.1. Definition in the homogeneous case 129
• 4.8.2. Semi-Markov backward processes in discrete time for the non-homogeneous case 130
• 4.8.3. DTSMP numerical solutions 133
• 4.9. Discrete time reward processes 137
• 4.9.1. Undiscounted SMRWP 137
• 4.9.2. Discounted SMRWP 141
• 4.9.3. General algorithms for DTSMRWP 144
• 4.10. Markov renewal functions in the homogeneous case 146
• 4.10.1. Entrance times 146
• 4.10.2. The Markov renewal equation 150
• 4.10.3. Asymptotic behavior of an MRP 151
• 4.10.4. Asymptotic behavior of SMP 153
• 4.11. Markov renewal equations for the non-homogeneous case 158
• 4.11.1. Entrance time 158
• 4.11.2. The Markov renewal equation 162
• CHAPTER 5. STOCHASTIC CALCULUS
• 165
• 5.1. Brownian motion 165
• 5.2. General definition of the stochastic integral 167
• 5.2.1. Problem of stochastic integration 167
• 5.2.2. Stochastic integration of simple predictable processes and semi-martingales 168
• 5.2.3. General definition of the stochastic integral 170
• 5.3. Ito s formula 177
• 5.3.1. Quadratic variation of a semi-martingale 177
• 5.3.2. Ito s formula 179
• 5.4. Stochastic integral with standard Brownian motion as an integrator process 180
• 5.4.1. Case of simple predictable processes 181
• 5.4.2. Extension to general integrator processes 183
• 5.5. Stochastic differentiation 184
• 5.5.1. Stochastic differential 184
• 5.5.2. Particular cases 184
• 5.5.3. Other forms of Ito s formula 185
• 5.6. Stochastic differential equations 191
• 5.6.1. Existence and unicity general theorem 191
• 5.6.2. Solution of stochastic differential equations 195
• 5.6.3. Diffusion processes 199
• 5.7. Multidimensional diffusion processes 202
• 5.7.1. Definition of multidimensional Ito and diffusion processes 203
• 5.7.2. Properties of multidimensional diffusion processes 203
• 5.7.3. Kolmogorov equations 205
• 5.7.4. The Stroock Varadhan martingale characterization of diffusion processes 208
• 5.8. Relation between the resolution of PDE and SDE problems. The Feynman Kac formula 209
• 5.8.1. Terminal payoff 209
• 5.8.2. Discounted payoff function 210
• 5.8.3. Discounted payoff function and payoff rate 210
• 5.9. Application to option theory 213
• 5.9.1. Options 213
• 5.9.2. Black and Scholes model 216
• 5.9.3. The Black and Scholes partial differential equation (BSPDE) and the BS formula 216
• 5.9.4. Girsanov theorem 219
• 5.9.5. The risk-neutral measure and the martingale property 221
• 5.9.6. The risk-neutral measure and the evaluation of derivative products 224
• CHAPTER 6. LEVY PROCESSES 227
• 6.1. Notion of characteristic functions 227
• 6.2. Levy processes 228
• 6.3. Levy Khintchine formula 230
• 6.4. Subordinators 234
• 6.5. Poisson measure for jumps 234
• 6.5.1. The Poisson random measure 234
• 6.5.2. The compensated Poisson process 235
• 6.5.3. Jump measure of a Levy process 236
• 6.5.4. The Ito Levy decomposition 236
• 6.6. Markov and martingale properties of Levy processes 237
• 6.6.1. Markov property 237
• 6.6.2. Martingale properties 239
• 6.6.3. Ito formula 240
• 6.7. Examples of Levy processes 240
• 6.7.1. The lognormal process: Black and Scholes process 240
• 6.7.2. The Poisson process 241
• 6.7.3. Compensated Poisson process 242
• 6.7.4. The compound Poisson process 242
• 6.8. Variance gamma (VG) process 244
• 6.8.1. The gamma distribution 244
• 6.8.2. The VG distribution 245
• 6.8.3. The VG process 246
• 6.8.4. The Esscher transformation 247
• 6.8.5. The Carr Madan formula for the European call 249
• 6.9. Hyperbolic Levy processes 250
• 6.10. The Esscher transformation 252
• 6.10.1. Definition 252
• 6.10.2. Option theory with hyperbolic Levy processes 253
• 6.10.3. Value of the European option call 255
• 6.11. The Brownian Poisson model with jumps 256
• 6.11.1. Mixed arithmetic Brownian Poisson and geometric Brownian Poisson processes 256
• 6.11.2. Merton model with jumps 258
• 6.11.3. Stochastic differential equation (SDE) for mixed arithmetic Brownian Poisson and geometric Brownian Poisson processes 261
• 6.11.4. Value of a European call for the lognormal Merton model 264
• 6.12. Complete and incomplete markets 264
• 6.13. Conclusion 265
• CHAPTER 7. ACTUARIAL EVALUATION, VAR AND STOCHASTIC INTEREST RATE MODELS 267
• 7.1. VaR technique 267
• 7.2. Conditional VaR value 271
• 7.3. Solvency II 276
• 7.3.1. The SCR indicator 276
• 7.3.2. Calculation of MCR 278
• 7.3.3. ORSA approach 279
• 7.4. Fair value 280
• 7.4.1. Definition 280
• 7.4.2. Market value of financial flows 281
• 7.4.3. Yield curve 281
• 7.4.4. Yield to maturity for a financial investment and a bond 283
• 7.5. Dynamic stochastic time continuous time model for instantaneous interest rate 284
• 7.5.1. Instantaneous deterministic interest rate 284
• 7.5.2. Yield curve associated with a deterministic instantaneous interest rate 285
• 7.5.3. Dynamic stochastic continuous time model for instantaneous interest rate 286
• 7.5.4. The OUV stochastic model 287
• 7.5.5. The CIR model 289
• 7.6. Zero-coupon pricing under the assumption of no arbitrage 292
• 7.6.1. Stochastic dynamics of zero-coupons 292
• 7.6.2. The CIR process as rate dynamic 295
• 7.7. Market evaluation of financial flows 298
• BIBLIOGRAPHY 301
• INDEX 309.
• (source: Nielsen Book Data)

This book presents basic stochastic processes, stochastic calculus including Levy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented. The authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.
(source: Nielsen Book Data)

• Probability and Stochastic Processes Probability Random variables and their distributions Mathematical expectation Joint distribution and independence Convergence of random variables Laplace transform and generating functions Examples of discrete distributions Examples of continuous distributions Stochastic processes Stopping times Conditional expectation
• Poisson Processes Introduction to Poisson processes Arrival and inter-arrival times of Poisson processes Conditional distribution of arrival times Poisson processes with different types of events Compound Poisson processes Nonhomogeneous Poisson processes
• Renewal Processes An introduction to renewal processes Renewal reward processes Queuing systems Queue lengths, waiting times, and busy periods Renewal equation Key renewal theorem Regenerative processes Queue length distribution and PASTA
• Discrete Time Markov Chains Markov property and transition probabilities Examples of discrete time Markov chains Multi-step transition and reaching probabilities Classes, recurrence, and transience Periodicity, class property, and positive recurrence Expected hitting time and hitting probability Stationary distribution Limiting properties
• Continuous Time Markov Chain Markov property and transition probability Transition rates Stationary distribution and limiting properties Birth and death processes Exponential queuing systems Time reversibility Hitting time and phase-type distributions Queuing systems with time-varying rates
• Brownian Motion and Beyond Brownian motion Standard Brownian motion and its maximum Conditional expectation and martingales Brownian motion with drift Stochastic integrals Ito's formula and stochastic differential equations A single stock market model
• Bibliography Index.
• (source: Nielsen Book Data)

Applied Stochastic Processes presents a concise, graduate-level treatment of the subject, emphasizing applications and practical computation. It also establishes the complete mathematical theory in an accessible way. After reviewing basic probability, the text covers Poisson processes, renewal processes, discrete- and continuous-time Markov chains, and Brownian motion. It also offers an introduction to stochastic differential equations. While the main applications described are queues, the book also considers other examples, such as the mathematical model of a single stock market. With exercises in most sections, this book provides a clear, practical introduction for beginning graduate students. The material is presented in a straightforward manner using short, motivating examples. In addition, the author develops the mathematical theory with a strong emphasis on probability intuition.
(source: Nielsen Book Data)

• Discrete-Time Markov Chains.- Stationary Distributions of a Markov Chain.- Continuous-Time Birth and Death Markov Chains.- Percolation.- A Cellular Automaton.- Continuous-Time Branching Random Walk.- The Contact Process on a Homogeneous Tree.- Appendix: Some Facts About Probabilities on Countable Spaces.- Applications to Population Biology.- References.
• (source: Nielsen Book Data)

The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a first course in stochastic processes. It guides the reader in a very clever manner from classical ideas to some of the most interesting modern results...All essential facts are presented with clear proofs, illustrated by beautiful examples. ..The book is well organized, has informative chapter summaries, and presents interesting exercises. The clear proofs are concentrated at the ends of the chapters making it easy to find the results. The style is a good balance of mathematical rigorosity and user-friendly explanation. -Biometric Journal This small book is well-written and well-organized...Only simple results are treated ...but at the same time many ideas needed for more complicated cases are hidden and in fact very close. The second part is a really elementary introduction to the area of spatial processes...All sections are easily readable and it is rather tentative for the reviewer to learn them more deeply by organizing a course based on this book. The reader can be really surprised seeing how simple the lectures on these complicated topics can be. At the same time such important questions as phase transitions and their properties for some models and the estimates for certain critical values are discussed rigorously...This is indeed a first course on stochastic processes and also a masterful introduction to some modern chapters of the theory. -Zentralblatt Math.
(source: Nielsen Book Data)

• 1. On the connection between discrete and continuous Wick calculus with an application to the fractional Black-Scholes model / C. Bender and P. Parczewski
• 2. Malliavin differentiability of a class of Feller-diffusions with relevance in Finance / C.-O. Ewald ... [at al.]
• 3. A stochastic integral for adapted and instantly independent stochastic processes / H.-H. Kuo, A. Sae-Tang and B. Szozda
• 4. Independence of some multiple Poisson stochastic integrals with variable-sign kernels / N. Privault
• 5. Strategies for differential games / W.H. Fleming and D. Hernandez-Hernandez
• 6. BSDE approach to non-zero-sum stochastic differential games of control and stopping / I. Karatzas and Q. Li
• 7. On optimal dividend strategies in insurance with a random time horizon / H. Albrecher and S. Thonhauser
• 8. Counterparty risk and the impact of collateralization in CDS contracts / T.R. Bielecki, I. Cialenco and I. Iyigunler
• 9. A modern view on Merton's jump-diffusion model / G.H.L. Cheang and C. Chiarella
• 10. Hedging portfolio loss derivatives with CDS's / A. Cousin and M. Jeanblanc
• 11. New analytic approximations for pricing spread options / J. van der Hoek and M.W. Korolkiewicz
• 12. On the Polynomial-Normal model and option pricing / H. Li and A. Melnikov
• 13. A functional transformation approach to interest rate modeling / S. Luo, J. Yan and Q. Zhang
• 14. S&P 500 index option surface drivers and their risk neutral and real world quadratic covariations / D.B. Madan
• 15. A dynamic portfolio approach to asset markets and monetary policy / E. Platen and W. Semmler
• 16. Mean-variance portfolio selection under regime-switching diffusion asset models: a two-time-scale limit / G. Yin and Y. Talafha
• 17. Existence and uniqueness of solutions for a partially observed stochastic control problem / A. Bensoussan ... [et al.]
• 18. Continuous control of piecewise deterministic Markov processes with long run average cost / O.L.V. Costa and F. Dufour
• 19. Stochastic linear-quadratic control revisited / T.E. Duncan
• 20. Optimization of stochastic uncertain systems: entropy rate functionals, minimax games and robustness / F. Rezaei, C.D. Charalambous and N.U. Ahmed
• 21. Gradient based policy optimization of constrained Markov decision processes / V. Krishnamurthy and F.J. Vazquez Abad
• 22. Parameter estimation of a regime-switching model using an inverse Stieltjes moment approach / X. Xi, M.R. Rodrigo and R.S. Mamon
• 23. An optimal inventory-price coordination policy / H. Zhang and Q. Zhang.

This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.
(source: Nielsen Book Data)

• Introduction.- Discrete-Time Markov Models.- Poisson Processes.- Continuous-Time Markov Models.- Generalized Markov Models.- Queueing Models.- Brownian Motion.
• (source: Nielsen Book Data)

This book provides a self-contained review of all the relevant topics in probability theory. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Carolina at Chapel Hill.
(source: Nielsen Book Data)

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, 4e, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: * Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications* Plentiful, completely updated problems* Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers* New chapters of stochastic differential equations and Brownian motion and related processes* Additional sections on Martingale and Poisson process . Realistic applications from a variety of disciplines integrated throughout the text. . Extensive end of chapter exercises sets, 250 with answers . Chapter 1-9 of the new edition are identical to the previous edition . New! Chapter 10 - Random Evolutions . New! Chapter 11- Characteristic functions and Their Applications.
(source: Nielsen Book Data)

• 1. Introduction
• 2. Conditional probability and conditional expectation
• 3. Markov chains: introduction
• 4. Long run behavior of Markov chains
• 5. Poisson processes
• 6. Continuous time Markov chains
• 7. Renewal phenomena
• 8. Brownian motion and related processes
• 9. Queueing systems
• 10. Random evolutions
• 11. Characteristic functions and their applications.

• Random Change of Time-- Integral Representations and Change of Time in Stochastic Integrals-- Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis-- Stochastic Exponential and Stochastic Logarithm. Cumulant Processes-- Processes with Independent Increments. Levy Processes-- Change of Measure. General Facts-- Change of Measure in Models Based on Levy Processes-- Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes-- Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case-- Martingale Measures in the Stochastic Theory of Arbitrage-- Change of Measure in Option Pricing-- Conditionally Brownian and Levy Processes. Stochastic Volatility Models.
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"Change of Time and Change of Measure" provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. Random change of time is a key to understanding the nature of various types of stochastic processes, and gives rise to interesting mathematical results and to insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, but also has a considerable role in insurance mathematics, in large deviation theory, and other fields. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. It is invaluable as a textbook for graduate-level courses and students or a handy reference for researchers and practitioners in financial mathematics and econometrics.
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• Introduction What in the World Is a Stochastic Process? How to Characterize a Stochastic Process What Do We Do with a Stochastic Process? Discrete-Time Markov Chains: Transient Behavior Definition and Characterization Examples DTMCs in Other Fields Marginal Distributions Occupancy Times Computation of Matrix Powers DTMCs: First Passage Times Definitions Cumulative Distribution Function of T Absorption Probabilities Expectation of T Generating Function and Higher Moments of T DTMCs: Limiting Behavior Exploring the Limiting Behavior by Examples Irreducibility and Periodicity Recurrence and Transience Determining Recurrence and Transience: Infinite DTMCs Limiting Behavior of Irreducible DTMCs Examples: Limiting Behavior of Infinite State-Space Irreducible DTMCs Limiting Behavior of Reducible DTMCs DTMCs with Costs and Rewards Reversibility Poisson Processes Exponential Distributions Poisson Process: Definitions Event Times in a Poisson Process Superposition and Splitting of Poisson Processes Non-Homogenous Poisson Process Compound Poisson Process Continuous-Time Markov Chains Definitions and Sample Path Properties Examples Transient Behavior: Marginal Distribution Transient Behavior: Occupancy Times Computation of P(t): Finite State-Space Computation of P(t): Infinite State-Space First-Passage Times Exploring the Limiting Behavior by Examples Classification of States Limiting Behavior of Irreducible CTMCs Limiting Behavior of Reducible CTMCs CTMCs with Costs and Rewards Phase-Type Distributions Reversibility Queueing Models Introduction Properties of General Queueing Systems Birth and Death Queues Open Queueing Networks Closed Queueing Networks Single Server Queues Retrial Queue Infinite Server Queue Renewal Processes Introduction Properties of N(t) The Renewal Function Renewal-Type Equation Key Renewal Theorem Recurrence Times Delayed Renewal Processes Alternating Renewal Processes Semi-Markov Processes Renewal Processes with Costs/Rewards Regenerative Processes Markov Regenerative Processes Definitions and Examples Markov Renewal Process and Markov Renewal Function Key Renewal Theorem for MRPs Extended Key Renewal Theorem Semi-Markov Processes: Further Results Markov Regenerative Processes Applications to Queues Diffusion Processes Brownian Motion Sample Path Properties of BM Kolmogorov Equations for Standard Brownian Motion First Passage Times Reflected SBM Reflected BM and Limiting Distributions BM and Martingales Cost/Reward Models Stochastic Integration Stochastic Differential Equations Applications to Finance Epilogue Appendix A: Probability of Events Appendix B: Univariate Random Variables Appendix C: Multivariate Random Variables Appendix D: Generating Functions Appendix E: Laplace--Stieltjes Transforms Appendix F: Laplace Transforms Appendix G: Modes of Convergence Appendix H: Results from Analysis
• Appendix I: Difference and Differential Equations Answers to Selected Problems References Index Exercises appear at the end of each chapter.
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Based on the author's more than 25 years of teaching experience, "Modeling and Analysis of Stochastic Systems, Second Edition" covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edition: a new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to finance; a more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processes; and, two appendices that collect relevant results from analysis and differential and difference equations. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations. A collection of MATLAB[registered]-based programs can be downloaded from the author's website and a solutions manual is available for qualifying instructors.
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• A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Stochastic Differential Equations.- The Fokker Planck Equation.- The Fokker Planck Equation in Several Dimensions.- Small Noise Approximations for Diffusion Processes.- The White Noise Limited.- Beyond the White Noise Limit.- Levy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Mestability, and Escape Problems.- Simulation of Stochastic Differential Equations.- References.- Bibliography.- Author Index.- Symbol Index.- Subject Index.
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This classic text and reference collects, in simple language and deductive form, the many formulae and methods that can be found in the scientific literature on stochastic methods. To be useful to students and practitioners as a practical tool, the book is written without excessive mathematical rigour, yet restricted to those methods and approximations thereof, that can be systematized and controlled in a quantitative way. Over time, new editions have been expanded in scope for a widening readership that now encompasses all of the quantitative natural and social sciences. This fourth edition has been thoroughly updated and restructured, and features a large amount of entirely new material, including but not limited to aspects of driven stochastic systems, the application and validity of simulation methods as well as applications to financial markets.
(source: Nielsen Book Data)