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Stochastic analysis and diffusion processes / Gopinath Kallianpur and P. Sundar.
Author
Kallianpur, G.
[Browse]
Format
Book
Language
English
Εdition
First edition.
Published/Created
Oxford, United Kingdom : Oxford University Press, 2014.
Description
xi, 352 pages ; 24 cm
Availability
Available Online
Oxford Scholarship - Oxford University Press: Mathematics
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA274 .K35 2014
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Details
Subject(s)
Diffusion processes
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Stochastic analysis
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Author
Sundar, P. (Padmanabhan)
[Browse]
Series
Oxford graduate texts in mathematics ; 24.
[More in this series]
Oxford graduate texts in mathematics ; 24
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Summary note
"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 Itô 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." -- Provided by publisher.
Bibliographic references
Includes bibliographical references and index.
Contents
Introduction to stochastic processes
Brownian motion and Wiener measure
Elements of martingale theory
Analytic tools for Brownian motion
Stochastic integration
Stochastic differential equations
The martingale problem
Probability theory and partial differential equations
Gaussian solutions
Jump Markov processes
Invariant measures and ergodicity
Large deviations for diffusions.
Show 9 more Contents items
ISBN
9780199657063 ((hbk.))
0199657068 ((hbk.))
9780199657070 ((pbk.))
0199657076 ((pbk.))
LCCN
2013943837
OCLC
869525197
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Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Stochastic Analysis and Diffusion Processes
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99125187740906421