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Stochastic analysis and diffusion processes /
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2014.
|
| Colección: | Oxford graduate texts in mathematics ;
24. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 100 | 1 | |a Kallianpur, G. | |
| 245 | 1 | 0 | |a Stochastic analysis and diffusion processes / |c Gopinath Kallianpur and P. Sundar. |
| 264 | 1 | |a Oxford : |b Oxford University Press, |c 2014. | |
| 300 | |a 1 online resource (368 pages) | ||
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| 490 | 1 | |a Oxford graduate texts in mathematics ; |v 24 | |
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Ito formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis. | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover ; Preface; Contents; 1 Introduction to Stochastic Processes; 1.1 The Kolmogorov Consistency Theorem; 1.2 The Language of Stochastic Processes; 1.3 Sigma Fields, Measurability, and Stopping Times; Exercises; 2 Brownian Motion; 2.1 Definition and Construction of Brownian Motion; 2.2 Essential Features of a Brownian Motion; 2.3 The Reflection Principle; Exercises; 3 Elements of Martingale Theory; 3.1 Definition and Examples of Martingales; 3.2 Wiener Martingales and the Markov Property; 3.3 Essential Results on Martingales; 3.4 The Doob-Meyer Decomposition. | |
| 505 | 8 | |a 3.5 The Meyer Process for L2-martingales3.6 Local Martingales; Exercises; 4 Analytical Tools for Brownian Motion; 4.1 Introduction; 4.2 The Brownian Semigroup; 4.3 Resolvents and Generators; 4.4 Pregenerators and Martingales; Exercises; 5 Stochastic Integration; 5.1 The Itô Integral; 5.2 Properties of the Integral; 5.3 Vector-valued Processes; 5.4 The Itô Formula; 5.5 An Extension of the Itô Formula; 5.6 Applications of the Itô Formula; 5.7 The Girsanov Theorem; Exercises; 6 Stochastic Differential Equations; 6.1 Introduction; 6.2 Existence and Uniqueness of Solutions. | |
| 505 | 8 | |a 6.3 Linear Stochastic Differential Equations6.4 Weak Solutions; 6.5 Markov Property; 6.6 Generators and Diffusion Processes; Exercises; 7 The Martingale Problem; 7.1 Introduction; 7.2 Existence of Solutions; 7.3 Analytical Tools; 7.4 Uniqueness of Solutions; 7.5 Markov Property of Solutions; 7.6 Further Results on Uniqueness; 8 Probability Theory and Partial Differential Equations; 8.1 The Dirichlet Problem; 8.2 Boundary Regularity; 8.3 Kolmogorov Equations: The Heuristics; 8.4 Feynman-Kac Formula; 8.5 An Application to Finance Theory; 8.6 Kolmogorov Equations; Exercises; 9 Gaussian Solutions. | |
| 505 | 8 | |a 9.1 Introduction9.2 Hilbert-Schmidt Operators; 9.3 The Gohberg-Krein Factorization; 9.4 Nonanticipative Representations; 9.5 Gaussian Solutions of Stochastic Equations; Exercises; 10 Jump Markov Processes; 10.1 Definitions and Basic Results; 10.2 Stochastic Calculus for Processes with Jumps; 10.3 Jump Markov Processes; 10.4 Diffusion Approximation; Exercises; 11 Invariant Measures and Ergodicity; 11.1 Introduction; 11.2 Ergodicity for One-dimensional Diffusions; 11.3 Invariant Measures for d-dimensional Diffusions; 11.4 Existence and Uniqueness of Invariant Measures; 11.5 Ergodic Measures. | |
| 505 | 8 | |a Exercises12 Large Deviations Principle for Diffusions; 12.1 Definitions and Basic Results; 12.2 Large Deviations and Laplace-Varadhan Principle; 12.3 A Variational Representation Theorem; 12.4 Sufficient Conditions for LDP; Exercises; Notes on Chapters; References; Index. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Diffusion processes. | |
| 650 | 0 | |a Stochastic analysis. | |
| 650 | 6 | |a Processus de diffusion. | |
| 650 | 6 | |a Analyse stochastique. | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Diffusion processes |2 fast | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 650 | 7 | |a Mathematics. |2 ukslc | |
| 700 | 1 | |a Sundar, P. |q (Padmanabhan) | |
| 776 | 0 | 8 | |i Print version: |a Kallianpur, G. |t Stochastic analysis and diffusion processes. Sundar, P. Sundar |z 9780199657070 |w (OCoLC)868966495 |
| 830 | 0 | |a Oxford graduate texts in mathematics ; |v 24. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=694198 |z Texto completo |
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