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Stochastic analysis and diffusion pr...

Kallianpur, G.

Stochastic analysis and diffusion processes /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic analysis and diffusion processes /Gopinath Kallianpur and P. Sundar.
Author:	Kallianpur, G.
other author:	Sundar, P.
Published:	Oxford, United Kingdom :Oxford University Press,2014.
Description:	xi, 352 p. ;24 cm.
Subject:	Diffusion processes.
ISBN:	0199657068 (hbk.)

Stochastic analysis and diffusion processes /
Kallianpur, G.

Stochastic analysis and diffusion processes /Gopinath Kallianpur and P. Sundar. - 1st ed. - Oxford, United Kingdom :Oxford University Press,2014. - xi, 352 p. ;24 cm. - Oxford graduate texts in mathematics ;24. - Oxford graduate texts in mathematics ;23..

Includes bibliographical references and index.

Introduction to stochastic processes -- Brownian motion -- 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.

"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." --

ISBN: 0199657068 (hbk.)

LCCN: 2013943837

Nat. Bib. No.: GBB398937bnb

Nat. Bib. Agency Control No.: 016529709UkSubjects--Topical Terms:

186291
Diffusion processes.

LC Class. No.: QA274 / .K338 2014

Dewey Class. No.: 519.233

Stochastic analysis and diffusion processes /
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020 $a 9780199657063 (hbk.)
020 $a 9780199657070 (pbk.)
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050 0 0 $a QA274 $b .K338 2014
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100 1 $a Kallianpur, G. $3 183071
245 1 0 $a Stochastic analysis and diffusion processes / $c Gopinath Kallianpur and P. Sundar.
250 $a 1st ed.
260 $a Oxford, United Kingdom : $b Oxford University Press, $c 2014.
300 $a xi, 352 p. ; $c 24 cm.
490 1 $a Oxford graduate texts in mathematics ; $v 24
504 $a Includes bibliographical references and index.
505 0 $a Introduction to stochastic processes -- Brownian motion -- 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.
520 $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 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." -- $c Provided by publisher.
650 0 $a Diffusion processes. $3 186291
650 0 $a Stochastic analysis. $3 183332
700 1 $a Sundar, P. $q (Padmanabhan) $3 452225
830 0 $a Oxford graduate texts in mathematics ; $v 23. $3 692089