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1. Applied stochastic analysis [2019]
 E, Weinan, 1963 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xxi, 305 pages ; 26 cm.
 Summary

 Fundamentals: Random variables Limit theorems Markov chains Monte Carlo methods Stochastic processes Wiener process Stochastic differential equations FokkerPlanck equation Advanced topics: Path integral Random fields Introduction to statistical mechanics Rare events Introduction to chemical reaction kinetics Appendix Bibliography Index.
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QA274.2 .E23 2019  Unknown 
2. Noncausal stochastic calculus [2017]
 Ogawa, Shigeyoshi, author.
 Tokyo : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 1 Introduction  Why the Causality?. 2 Preliminary  Causal calculus. 3 Noncausal Calculus. 4 Noncausal Integral and Wiener Chaos. 5 Noncausal SDEs. 6 Brownian Particle Equation. 7 Noncausal SIE. 8 Stochastic Fourier Transformation. 9 Appendices to Chapter 2. 10 Appendices 2  Comments and Proofs. Index.
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 Cham, Switzerland : Birkhäuser, [2017]
 Description
 Book — vii, 221 pages : illustrations (some color) ; 25 cm.
 Summary

 Preface. Positivehomogeneous operators, heat kernel estimates and the LegendreFenchel transform. Strong stability of heat Kernels of nonsymmetric stablelike operators. Multiplicative functional for the heat equation on manifolds with boundary. Connections between the Dirichlet and the Neumann problem for continuous and integrable boundary data. Decomposition and limit theorems for a class of selfsimilar Gaussian processes. On a priori estimates for rough PDES. Levy systems and moment formulas for mixed Poisson integrals. Conformal transforms and Doob's hprocesses on Heisenberg Groups. On the Macroscopic Fractal Geometry of Some Random Sets. Critical behavior of meanfield XY and related models.
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QA274.2 .S77145 2017  Unknown 
 Matsumoto, Hiroyuki, 1946 author.
 New York : Cambridge University Press, 2017.
 Description
 Book — xii, 346 pages ; 24 cm.
 Summary

 Preface
 Frequently used notation
 1. Fundamentals of continuous stochastic processes
 2. Stochastic integrals and Ito's formula
 3. Brownian motion and Laplacian
 4. Stochastic differential equations
 5. Malliavin calculus
 6. BlackScholes model
 7. Semiclassical limit
 Appendix
 References
 Subject index.
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QA274.2 .M386 2017  Unknown 
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2014.
 Description
 Book — xiv, 561 p.
 Summary

 Gaussian Measures on Infinite Dimensional Spaces
 Hypergroups and Random Fields
 A Concise Exposition of Large Deviations
 Quantum White Noise Calculus and Applications
 Weak Radon  Nikodym Derivatives, Dunford  Schwartz Type Integration, and Cramer and Karhunen Processes
 Entropy, SDE  LDP and Fenchel  Legendre  Orlicz Classes
 Bispectral Density Estimation in Harmonizable Processes.
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6. Introduction to stochastic analysis [electronic resource] : integrals and differential equations [2013]
 Mackevičius, Vigirdas.
 London : Wiley, 2013.
 Description
 Book — 1 online resource (278 pages).
 Summary

 Preface 9 Notation 13
 Chapter 1. Introduction: Basic Notions of Probability Theory 17 1.1. Probability space 17 1.2. Random variables 21 1.3. Characteristics of a random variable 21 1.4. Types of random variables 23 1.5. Conditional probabilities and distributions 26 1.6. Conditional expectations as random variables 27 1.7. Independent events and random variables 29 1.8. Convergence of random variables 29 1.9. Cauchy criterion 31 1.10. Series of random variables 31 1.11. Lebesgue theorem 32 1.12. Fubini theorem 32 1.13. Random processes 33 1.14. Kolmogorov theorem 34
 Chapter 2. Brownian Motion 35 2.1. Definition and properties 35 2.2. White noise and Brownian motion 45 2.3. Exercises 49
 Chapter 3. Stochastic Models with Brownian Motion and White Noise 51 3.1. Discrete time 51 3.2. Continuous time 55
 Chapter 4. Stochastic Integral with Respect to Brownian Motion 59 4.1. Preliminaries. Stochastic integral with respect to a step process 59 4.2. Definition and properties 69 4.3. Extensions 81 4.4. Exercises 85
 Chapter 5. Ito s Formula 87 5.1. Exercises 94
 Chapter 6. Stochastic Differential Equations 97 6.1. Exercises 105
 Chapter 7. Ito Processes 107 7.1. Exercises 121
 Chapter 8. Stratonovich Integral and Equations 125 8.1. Exercises 136
 Chapter 9. Linear Stochastic Differential Equations 137 9.1. Explicit solution of a linear SDE 137 9.2. Expectation and variance of a solution of an LSDE 141 9.3. Other explicitly solvable equations 145 9.4. Stochastic exponential equation 147 9.5. Exercises 153
 Chapter 10. Solutions of SDEs as Markov Diffusion Processes 155 10.1. Introduction 155 10.2. Backward and forward Kolmogorov equations 161 10.3. Stationary density of a diffusion process 172 10.4. Exercises 176
 Chapter 11. Examples 179 11.1. Additive noise: Langevin equation 180 11.2. Additive noise: general case 180 11.3. Multiplicative noise: general remarks 184 11.4. Multiplicative noise: Verhulst equation 186 11.5. Multiplicative noise: genetic model 189
 Chapter 12. Example in Finance: Black Scholes Model 195 12.1. Introduction: what is an option? 195 12.2. Selffinancing strategies 197 12.3. Option pricing problem: the Black Scholes model 204 12.4. Black Scholes formula 206 12.5. Riskneutral probabilities: alternative derivation of Black Scholes formula 210 12.6. Exercises 214
 Chapter 13. Numerical Solution of Stochastic Differential Equations 217 13.1. Memories of approximations of ordinary differential equations 218 13.2. Euler approximation 221 13.3. Higherorder strong approximations 224 13.4. Firstorder weak approximations 231 13.5. Higherorder weak approximations 238 13.6. Example: Milsteintype approximations 241 13.7. Example: Runge Kutta approximations 244 13.8. Exercises 249
 Chapter 14. Elements of Multidimensional Stochastic Analysis 251 14.1. Multidimensional Brownian motion 251 14.2. Ito s formula for a multidimensional Brownian motion 252 14.3. Stochastic differential equations 253 14.4. Ito processes 254 14.5. Ito s formula for multidimensional Ito processes 256 14.6. Linear stochastic differential equations 256 14.7. Diffusion processes 257 14.8. Approximations of stochastic differential equations 259 Solutions, Hints, and Answers 261 Bibliography 271 Index 273.
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7. Discretization of processes [2012]
 Jacod, Jean.
 Heidelberg ; New York : SpringerVerlag Berlin Heidelberg, c2012.
 Description
 Book — xiv, 596 p. : ill. ; 24 cm.
 Summary

 Part I Introduction and Preliminary Material. 1.Introduction
 2.Some Prerequisites. Part II The Basic Results. 3.Laws of Large Numbers: the Basic Results. 4.Central Limit Theorems: Technical Tools. 5.Central Limit Theorems: the Basic Results. 6.Integrated Discretization Error. Part III More Laws of Large Numbers. 7.First Extension: Random Weights. 8.Second Extension: Functions of Several Increments. 9.Third Extension: Truncated Functionals. Part IV Extensions of the Central Limit Theorems. 10.The Central Limit Theorem for Random Weights. 11.The Central Limit Theorem for Functions of a Finite Number of Increments. 12.The Central Limit Theorem for Functions of an Increasing Number of Increments. 13.The Central Limit Theorem for Truncated Functionals. Part V Various Extensions. 14.Irregular Discretization Schemes. 15.Higher Order Limit Theorems. 16.Semimartingales Contaminated by Noise. Appendix. References. Assumptions. Index of Functionals. Index.
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QA274.2 .J33 2012  Unknown 
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2012.
 Description
 Book — xx, 437 p. : ill. (some col.)
 Summary

 Stochastic Geometric PDEs (Z Brzezniak et al.)
 Rough Paths on Manifolds (T Cass et al.)
 Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations (J Q Duan et al.)
 Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations (J Q Duan et al.)
 A BurgersZeldovich Model for the Formation of Planetesimals via Nelson's Stochastic Mechanics (R Durran et al.)
 Two Problems Concerning Brownian Motion on a Complete Riemannian Manifold (E P Hsu)
 Sticky Shuffle Product Hopf Algebras and Their Stochastic Representations (R Hudson)
 Chain Rules for Levy Flows and Kolmogorov Equations for Associated JumpDiffusions (H Kunita)
 The Stochastic Differential Equation Approach to Analysis on Path Space (XM Li)
 Pathwise Properties of Random Quadratic Mapping (P Lian & H Z Zhao)
 Invariant Manifolds for Infinite Dimensional Random Dynamical Systems (K N Lu & B Schmalfuss)
 Some Topics on Dirichlet Forms (Z M Ma & W Sun)
 Hamilton  Jacobi Theory and the Stochastic Elementary Formula (A Neate & A Truman).
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 www.worldscientific.com World Scientific
 Google Books (Full view)
9. Stochastic processes [2011]
 Bass, Richard F.
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Description
 Book — xv, 390 p. : ill. ; 26 cm.
 Summary

 Preface
 1. Basic notions
 2. Brownian motion
 3. Martingales
 4. Markov properties of Brownian motion
 5. The Poisson process
 6. Construction of Brownian motion
 7. Path properties of Brownian motion
 8. The continuity of paths
 9. Continuous semimartingales
 10. Stochastic integrals
 11. Ito's formula
 12. Some applications of Ito's formula
 13. The Girsanov theorem
 14. Local times
 15. Skorokhod embedding
 16. The general theory of processes
 17. Processes with jumps
 18. Poisson point processes
 19. Framework for Markov processes
 20. Markov properties
 21. Applications of the Markov properties
 22. Transformations of Markov processes
 23. Optimal stopping
 24. Stochastic differential equations
 25. Weak solutions of SDEs
 26. The RayKnight theorems
 27. Brownian excursions
 28. Financial mathematics
 29. Filtering
 30. Convergence of probability measures
 31. Skorokhod representation
 32. The space C[0, 1]
 33. Gaussian processes
 34. The space D[0, 1]
 35. Applications of weak convergence
 36. Semigroups
 37. Infinitesimal generators
 38. Dirichlet forms
 39. Markov processes and SDEs
 40. Solving partial differential equations
 41. Onedimensional diffusions
 42. Levy processes
 A. Basic probability
 B. Some results from analysis
 C. Regular conditional probabilities
 D. Kolmogorov extension theorem
 E. Choquet capacities
 Frequently used notation
 Index.
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QA274.2 .B375 2011  Unknown 
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2010.
 Description
 Book — xvi, 291 p. : ill. (some col.)
 Summary

 Introduction: Stochastic Analysis and Stochastic Dynamics
 A Glimpse of Stochastic Dynamical Systems
 Progress in White Noise Analysis
 Dynamical Systems Driven by Fractional Brownian Motion
 Dynamical Systems Driven by NonGaussian Noise
 Stochastic Dynamical Systems with Memory
 Simulation of Stochastic Dynamical Systems.
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 www.worldscientific.com World Scientific
 Google Books (Full view)
 Cambridge, UK ; New York : Cambridge University Press, 2009.
 Description
 Book — vi, 390 p. : ill. ; 23 cm.
 Summary

 Preface Part I. Foundations and techniques in stochastic analysis: 1. Random variables  without basic space Goetz Kersting 2. Chaining techniques and their application to stochastic flows Michael Scheutzow 3. Ergodic properties of a class of nonMarkovian processes Martin Hairer 4. Why study multifractal spectra? Peter Moerters Part II. Construction, simulation, discretisation of stochastic processes: 5, Construction of surface measures for Brownian motion Nadia Sidorova and Olaf Wittich 6. Sampling conditioned diffusions Martin Hairer, Andrew Stuart and Jochen Vo
 7. Coding and convex optimization problems Steffen Dereich Part III. Stochastic analysis in mathematical physics: 8. Intermittency on catalysts Jurgen Gartner, Frank den Hollander and Gregory Maillard 9. Stochastic dynamical systems in infinite dimensions SalahEldin A. Mohammed 10. Feynman formulae for evolutionary equations Oleg G.Smolyanov 11. Deformation quantization in infinite dimensional analysis Remi Leandre Part IV. Stochastic analysis in mathematical biology: 12. Measurevalued diffusions, coalescents and genetic inference Matthias Birkner and Jochen Blath 13. How often does the ratchet click? Facts, heuristics, asymptotics Alison M. Etheridge, Peter Pfaffelhuber and Anton Wakolbinger.
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QA274.2 .T74 2009  Unknown 
 International Conference on Mathematical Analysis of Random Phenomena (2005 : Hammamet)
 Singapore ; Hackensack, N.J. : World Scientific, c2007.
 Description
 Book — vii, 231 p. : ill.
 Summary

 Geometry and integration by parts on H \ Diff(S1)
 Invariant measures for OrnsteinUhlenbeck operators
 Backward stochastic differential equations with respect to martingales
 Partial unitarity arising from quadratic quantum white noise
 Schilder's theorem for Gaussian white noise distributions
 A nonlinear stochastic equation of convolution type
 Variational principle for diffusions on the diffeomorphism group with the H2 metric
 On a variational principle for the NavierStokes equation
 Convolution calculus on white noise spaces and Feynman graph representation of generalized renormalization flows
 Characterizations of standard noises and applications
 Analysis of stable white noise functionals
 Unitarizing measures for a representation of the Virasoro algebra, according to Kirillov and Malliavin: state of the problem
 FKG inequality on the Wiener space via predictable representation
 Pathintegral estimates of groundstate functionals
 A representation theorem and a sensitivity result for functionals of jump diffusions
 Creation and annihilation operators on locally compact spaces
 From the geometry of parabolic PDE to the geometry of SDE.
13. Combinatorial stochastic processes : École d'Été de Probabilités de SaintFlour XXXII  2002 [2006]
 Pitman, Jim.
 Berlin ; New York : SpringerVerlag, 2006.
 Description
 Book — ix, 256 p. : ill. ; 24 cm.
 Summary

 Preliminaries. Bell polynomials, composite structures and Gibbs partitions.Exchangeable random partitions. Sequential constructions of random partitions. Poisson constructions of random partitions. Coagulation and fragmentation processes. Random walks and random forests. The Brownian forest. Brownian local times, branching and Bessel processes. Brownian bridge asymptotics for random mappings. Random forests and the additive coalescent. Bibliography. Index.
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Shelved by Series title V.1875  Unknown 
 Boston : Birkhäuser, c2004.
 Description
 Book — viii, 405 p. : ill. ; 24 cm.
 Summary

 Preface. Rao: Introduction and Outline. Bell: Stochastic Differential Equations and Hypoelliptic Operators. Driver: Curved Wiener Space Analysis. Gudder: Noncommutative Probability and Applications. Jefferies: Advances and Applications of the Feynman Integral. Kunita: Stochastic Differential Equations Based on Levy Processes and Stochastic Flows of Diffeomorphisms. Rao: Convolutions of Vector Fields  II: Amenability and Spectral Properties. Index.
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QA274.2 .R423 2004  Available 
15. Stochastic analysis [2004]
 Kakuritsu kaiseki. English
 Shigekawa, Ichirō, 1953
 Providence, R.I. : American Mathematical Society, c2004.
 Description
 Book — xii, 182 p. ; 22 cm.
 Summary

 Wiener space OrensteinUhlenbeck process The LittlewoodPaleyStein inequality Sobolev spaces on an abstrct Wiener space Absolute continuity of distributions and smoothness of density functions Application to stochastic differential equations Perspectives on current research Bibliography Index.
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QA274.2 .S4813 2004  Unknown 
 New York : Marcel Dekker, c2002.
 Description
 Book — xvii, 763 p. ; 26 cm.
 Summary

 Markov processes and their applications
 semimartingale theory and stochastic calculus
 white noise theory
 stochastic differential equations and its applications
 large deviations and applications
 a brief introduction to numerical analysis of (ordinary) stochastic differential equations without tears
 stochastic differential games and applications
 stability and stabilizing control of stochastic systems
 stochastic approximation  theory and applications
 stochastic manufacturing systems
 optimization by stochastic methods
 stochastic control methods in asset pricing.
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QA274.2 .H36 2002  Unknown 
 Boston : Kluwer Academic Publishers, c2002.
 Description
 Book — xxviii, 770 p. : ill. ; 25 cm.
 Summary

 Preface. Contributing Authors. 1. Professor Sidney J. Yakowitz
 D.S. Yakowitz. Part I. 2. Stability of Single Class Queueing Networks
 H.J. Kushner. 3. Sequential Optimization Under Uncertainty
 Tze Leung Lai. 4. Exact Asymptotics for Large Deviation Probabilities, with Applications
 I. Pinelis. Part II. 5. Stochastic Modelling of Early HIV Immune Responses Under Treatment by Protease Inhibitors
 WaiYuang Tan, Zhihuo Xiang. 6. The impact of reusing hypodermic needles
 B. Barnes, J. Gani. 7. Nonparametric Frequency Detection and Optimal Coding in Molecular Biology
 D.S. Stoffer. Part III. 8. An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems
 A. Nemirovski, R.Y. Rubinstein. 9. Regression Models for Binary Time Series
 B. Kedem, K. Fokianos. 10. Almost Sure Convergence Properties of NadarayaWatson Regression Estimates
 H. Walk. 11. Strategies for Sequential Prediction of Stationary Time Series
 L. Gyorfi, G. Lugosi. Part IV. 12. The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lag
 C. Chiarella, F. Szidarovszky. 13. A Differential Game of Debt Contract Valuation
 A. Haurie, F. Moresino. 14. Huge Capacity Planning and Resource Pricing for Pioneering Projects
 D. Porter. 15. Affordable Upgrades of Complex Systems: A Multilevel, PerformanceBased Approach
 J.A. Reneke, et al. 16. On Successive Approximation of Optimal Control of Stochastic Dynamic Systems
 FeiYue Wang, G.N. Saridis. 17. Stability of Random Iterative Mappings
 L. Gerencser. Part V. 18. `Unobserved' Monte Carlo Methods for Adaptive Algorithms
 V. Solo. 19. Random Search Under Additive Noise
 L. Devroye, A. Krzyzak. 20. Recent Advances in Randomized QuasiMonte Carlo Methods
 P. L'Ecuyer, C. Lemieux. Part VI. 21. Singularly Perturbed Markov Chains and Applications to LargeScale Systems under Uncertainty
 G. Yin, et al. 22. RiskSensitive Optimal Control in Communicating Average Markov Decision Chains
 R. CavazosCadena, E. FernandezGaucherand. 23. Some Aspects of Statistical Inference in a Markovian and Mixing Framework
 G.G. Roussas. Part VII. 24. Stochastic Ordening of Order Statistics II
 P.J. Boland, et al. 25. Vehicle Routing with Stochastic Demands: Models & Computational Methods
 M. Dror. 26. Life in the Fast Lane: Yates's Algorithm, Fast Fourier and Walsh Transforms
 P.J. Sanchez, et al. 27. Uncertainty Bounds in Parameter Estimation with Limited Data
 J.C. Spall. 28. A Tutorial on Hierarchical Lossless Data Compression
 J.C. Kieffer. Part VIII. 29. Eureka! Bellman's Principle of Optimality is valid!
 M. Sniedovich. 30. Reflections on Statistical Methods for Complex Stochastic Systems
 M.F. Neuts. Author Index.
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QA274.2 .M63 2002  Available 
 Grigoriu, Mircea.
 Boston : Birkhäuser, c2002.
 Description
 Book — xii, 774 p. : ill. ; 24 cm.
 Summary

 Introduction * Probability Theory * Stochastic Processes * Ito's Formula and Stochastic Differential Equations * Monte Carlo Simulation * Deterministic System and Input * Deterministic System and Stochastic Input * Stochastic System and Deterministic Input * Stochastic System and Stochastic Input * Bibliography * Index.
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QA274.2 .G75 2002  Unknown 
19. Chaos : a statistical perspective [2001]
 Chan, Kungsik.
 New York : Springer, c2001.
 Description
 Book — xiv, 300 p. : ill. (some col.) ; 24 cm.
 Summary

 1. Introduction
 2. Deterministic chaos
 3. Chaos and Stochastic Systems
 4. Statistical Analysis I
 5. Statistical Analysis II
 6. Nonlinear LeastSquare Prediction
 7. Miscellaneous Topics
 References.
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QA274.2 .C53 2001  Available 
 Mikosch, Thomas.
 Singapore ; River Edge, N.J. : World Scientific Publ., c1998 (2003 printing)
 Description
 Book — ix, 212 p. : ill. ; 23 cm.
 Summary

 Preliminaries  basic concepts from probability theory
 stochastic processes
 Brownian motion
 conditional expectation
 Martingales
 the stochastic integral  the Riemann and RiemannStieltjes
 integrals
 the Ito integral
 the Ito lemma
 the Stratonovich and other integrals
 stochastic differential equations  deterministic differential equations
 Ito stochastic differential equations
 the general linear differential equation
 numerical solution
 applications of stochastic calculus in finance  the BlackScholes optionpricing formula
 a useful technique  change of measure. Appendices: modes of convergence
 inequalities
 nondifferentiability and unbounded variation of Brownian sample paths
 proof of the existence of the general Ito stochastic integral
 the RadonNikodym theorem
 proof of the existence and uniqueness of the conditional expectation.
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QA274.2 .M54 1998  Unknown 
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