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Stochastic analysis and stochastic differential equations are rapidly developing fields in probability theory and its applications. This book provides a systematic treatment of stochastic differential equations and stochastic flow of diffeomorphisms and describes the properties of stochastic flows. Professor Kunita's approach regards the stochastic differential equation as a dynamical system driven by a random vector field, including K. Ito's classical theory. Beginning with a discussion of Markov processes, martingales and Brownian motion, Kunita reviews Ito's stochastic analysis. He places...