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Stochastic Analysis and Diffusion Processes - Oxford Scholarship Online
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Stochastic Analysis and Diffusion Processes

Gopinath Kallianpur and P Sundar


Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local martingales are discussed. The book proceeds to construct stochastic integrals, prove the Itô formula, derive several important applications of the formula such as the martingale representation theorem and the Burkhölder-Davis-Gundy inequality, and establish the Girsanov theorem on change of measures. Next, attention is focused on stochastic differential equations which arise in modeling physical phenome ... More

Keywords: Brownian motion, martingale, stochastic integral, stochastic differential equation, diffusion process, martingale problem, jump Markov process, invariant measure, large deviations principle

Bibliographic Information

Print publication date: 2014 Print ISBN-13: 9780199657063
Published to Oxford Scholarship Online: April 2014 DOI:10.1093/acprof:oso/9780199657063.001.0001


Affiliations are at time of print publication.

Gopinath Kallianpur, author
Professor Emeritus, Department of Statistics, University of North Carolina at Chapel Hill

P Sundar, author
Professor of Mathematics, Department of Mathematics, Louisiana State University