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 Venkateswarlu, Ch.
 Amsterdam : Elsevier, c2020.
 Description
 Book — 1 online resource (312 p.)
 Summary

 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.
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 Rao, M. M. (Malempati Madhusudana), 1929 author.
 1st edition  Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2020]
 Description
 Book — 1 online resource
 Summary

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, CramerKarhunen 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.
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 Bas, Esra, author.
 Cham : Springer, [2019]
 Description
 Book — 1 online resource
 Summary

 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 DiscreteTime Markov Chains. ContinuousTime Markov Chains. An Introduction to Queueing Models. Introduction to Brownian Motion. Basics of Martingales. Basics of Reliability Theory.
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 Stanimirović, Ivan.
 Ashland : Arcler Press, 2019.
 Description
 Book — 1 online resource (255 pages)
 Summary

 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 ContinuousTime 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
 Masoliver, Jaume, 1951 author.
 Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018]
 Description
 Book — 1 online resource.
 Summary

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 mediumlevel 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 socioeconomic systems.
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 Cham : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 0. Preface. List of contributors.
 1. Youri Davydov, Valentin Konakov, Roberto Garra and Enzo Orsingher: Random motions.
 2. Aurelien Alfonsi, Masafumi Hayashi, Arturo KohatsuHiga, 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.
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 Pipiras, Vladas author.
 Cham : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 Preliminaries. Minimality, Rigidity, and Flows. Mixed Moving Averages and Selfsimilarity. A. Historical Notes. B. Standard Lebesgue Spaces and Projections. C. Notation Summary.
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8. Stochastic Processes [2017]
 Borodin, A. N., author.
 Cham, Switzerland : Birkhäuser, [2017]
 Description
 Book — 1 online resource.
 Summary

 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 nfold differentiation. Bibliography. Subject index.
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9. Recueil de Modèles Aléatoires [2016]
 Chafaï, Djalil, author.
 Berlin : Springer, 2016.
 Description
 Book — 1 online resource (xiii, 398 pages) : illustrations. Digital: text file; PDF.
 Summary

 Avantpropos
 Pile, face, coupons
 Marches aléatoires
 Branchement et processus de GaltonWatson
 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 WrightFisher
 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'OrnsteinUhlenbeck
 Modèles de diffusion cinétique
 Des chaînes de Markov aux processus de diffusion
 Suggestions bibliographiques
 Littérature
 Index
 Principales notations et abréviations.
10. Basic stochastic processes [2015]
 Devolder, Pierre.
 London : ISTE ; Hoboken, NJ : Wiley, c2015.
 Description
 Book — xii, 310 p. : ill. ; 24 cm.
 Summary

 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. Multidimensional 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 NONHOMOGENEOUS RENEWAL MODELS 47
 2.1. Introduction 47
 2.2. Continuous time nonhomogeneous convolutions 49
 2.2.1. Nonhomogeneous convolution product 49
 2.3. Homogeneous and nonhomogeneous 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. Nonhomogeneous case 68
 2.8. Homogeneous alternating renewal processes 69
 2.9. Solution of nonhomogeneous 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. Nonhomogeneous 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. Nonhomogeneous MRWP 112
 CHAPTER 4. HOMOGENEOUS AND NONHOMOGENEOUS SEMIMARKOV MODELS 113
 4.1. Continuous time semiMarkov processes 113
 4.2. The embedded Markov chain 117
 4.3. The counting processes and the associated semiMarkov 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 zeroorder (PYKE (1962)) 122
 4.5.3. Continuous Markov processes 124
 4.6. Examples 124
 4.7. Discrete time homogeneous and nonhomogeneous semiMarkov processes 127
 4.8. SemiMarkov backward processes in discrete time 129
 4.8.1. Definition in the homogeneous case 129
 4.8.2. SemiMarkov backward processes in discrete time for the nonhomogeneous 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 nonhomogeneous 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 semimartingales 168
 5.2.3. General definition of the stochastic integral 170
 5.3. Ito s formula 177
 5.3.1. Quadratic variation of a semimartingale 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 riskneutral measure and the martingale property 221
 5.9.6. The riskneutral 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. Zerocoupon pricing under the assumption of no arbitrage 292
 7.6.1. Stochastic dynamics of zerocoupons 292
 7.6.2. The CIR process as rate dynamic 295
 7.7. Market evaluation of financial flows 298
 BIBLIOGRAPHY 301
 INDEX 309.
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QA274 .D475 2015  Unknown 
11. Applied stochastic processes [2014]
 Liao, Ming (Mathematician), author.
 Boca Raton : CRC Press, [2014]
 Description
 Book — viii, 199 pages : illustrations ; 25 cm
 Summary

 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 interarrival 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 Multistep 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 phasetype distributions Queuing systems with timevarying 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.
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QA274 .L52 2014  Unknown 
 Schinazi, Rinaldo B. (Rinaldo Bruno), author.
 Second edition.  New York, NY : Birkhäuser, 2014.
 Description
 Book — 1 online resource (xii, 268 pages) : illustrations (some color) Digital: text file; PDF.
 Summary

 DiscreteTime Markov Chains. Stationary Distributions of a Markov Chain. ContinuousTime Birth and Death Markov Chains. Percolation. A Cellular Automaton. ContinuousTime Branching Random Walk. The Contact Process on a Homogeneous Tree. Appendix: Some Facts About Probabilities on Countable Spaces. Applications to Population Biology. References.
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13. Diffusion processes and stochastic calculus [2014]
 Baudoin, Fabrice.
 Zurich, Switzerland : European Mathematical Society, [2014]
 Description
 Book — ix, 276 pages ; 24 cm.
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QA274 .B397 2014  Unknown 
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2012.
 Description
 Book — xvi, 588 p. : ill. (some col.)
 Summary

 1. On the connection between discrete and continuous Wick calculus with an application to the fractional BlackScholes model / C. Bender and P. Parczewski
 2. Malliavin differentiability of a class of Fellerdiffusions with relevance in Finance / C.O. Ewald ... [at al.]
 3. A stochastic integral for adapted and instantly independent stochastic processes / H.H. Kuo, A. SaeTang and B. Szozda
 4. Independence of some multiple Poisson stochastic integrals with variablesign kernels / N. Privault
 5. Strategies for differential games / W.H. Fleming and D. HernandezHernandez
 6. BSDE approach to nonzerosum 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 jumpdiffusion 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 PolynomialNormal 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. Meanvariance portfolio selection under regimeswitching diffusion asset models: a twotimescale 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 linearquadratic 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 regimeswitching model using an inverse Stieltjes moment approach / X. Xi, M.R. Rodrigo and R.S. Mamon
 23. An optimal inventoryprice coordination policy / H. Zhang and Q. Zhang.
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 www.worldscientific.com World Scientific
 Google Books (Full view)
 Kulkarni, Vidyadhar G.
 2nd ed.  New York : Springer Science+Business Media, LLC, 2011.
 Description
 Book — 1 online resource (xiii, 313 pages) : illustrations.
 Summary

 Introduction. DiscreteTime Markov Models. Poisson Processes. ContinuousTime Markov Models. Generalized Markov Models. Queueing Models. Brownian Motion.
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16. An introduction to stochastic modeling [2011]
 Pinsky, Mark A., 1940
 4th ed.  Amsterdam ; Boston : Academic Press, c2011.
 Description
 Book — xiv, 563 p. : ill. ; 24 cm.
 Summary

Serving as the foundation for a onesemester 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 endofchapter 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 19 of the new edition are identical to the previous edition . New! Chapter 10  Random Evolutions . New! Chapter 11 Characteristic functions and Their Applications.
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QA274 .T35 2011  Unknown 
QA274 .T35 2011  Unknown 
17. An introduction to stochastic modeling [2011]
 Pinsky, Mark A., 1940
 4th ed.  Amsterdam ; Boston : Academic Press, ©2011.
 Description
 Book — 1 online resource (xiv, 563 pages) : illustrations.
 Summary

 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.
18. Change of time and change of measure [2010]
 BarndorffNielsen, O. E. (Ole E.)
 Hackensack, N.J. : World Scientific, c2010.
 Description
 Book — xvi, 305 p. ; 24 cm.
 Summary

 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 Discretetime 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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QA274 .B36 2010  Available 
19. Modeling and analysis of stochastic systems [2010]
 Kulkarni, Vidyadhar G.
 2nd ed.  Boca Raton : CRC Press, c2010.
 Description
 Book — xxi, 542 p. : ill. ; 25 cm.
 Summary

 Introduction What in the World Is a Stochastic Process? How to Characterize a Stochastic Process What Do We Do with a Stochastic Process? DiscreteTime 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 StateSpace 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 NonHomogenous Poisson Process Compound Poisson Process ContinuousTime Markov Chains Definitions and Sample Path Properties Examples Transient Behavior: Marginal Distribution Transient Behavior: Occupancy Times Computation of P(t): Finite StateSpace Computation of P(t): Infinite StateSpace FirstPassage 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 PhaseType 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 RenewalType Equation Key Renewal Theorem Recurrence Times Delayed Renewal Processes Alternating Renewal Processes SemiMarkov 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 SemiMarkov 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: LaplaceStieltjes 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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QA274 .K844 2010  Unknown 
 Gardiner, C. W. (Crispin W.), 1942
 4th ed.  Berlin ; London : Springer, 2009.
 Description
 Book — xvii, 447 p. : ill. ; 24 cm.
 Summary

 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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SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request (opens in new tab) 
QA274 .G37 2009  Available 
Articles+
Journal articles, ebooks, & other eresources
Guides
Course and topicbased guides to collections, tools, and services.