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Stochastic Analysis and Diffusion Processes$
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Gopinath Kallianpur and P Sundar

Print publication date: 2014

Print ISBN-13: 9780199657063

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199657063.001.0001

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Stochastic Differential Equations

Stochastic Differential Equations

(p.134) 6 Stochastic Differential Equations
Stochastic Analysis and Diffusion Processes

Gopinath Kallianpur

P. Sundar

Oxford University Press

Stochastic differential equations arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of stochastic differential equations and form the main theme of this book. The existence of a unique strong solution of a stochastic differential equation is proved under suitable conditions. Explicit solutions of a class of equations are shown. Next, weak solutions of stochastic differential equations, uniqueness in law, and the results of Yamada-Watanabe are presented. The Markov property of solutions and diffusion processes are studied.

Keywords:   stochastic differential equation, strong solution, pathwise uniqueness, weak solution, uniqueness in law, Yamada-Watanabe theorem, Markov property, diffusion process

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