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. Itô's classical theory. Beginning with a discussion
of Markov processes, martingales and Brownian motion, Kunita reviews
Itô's stochastic analysis. He places emphasis on establishing that the
solution defines a flow of diffeomorphisms. This flow property is basic
in the modern and comprehensive analysis of the solution and will be
applied to solve the first and second order stochastic partial
differential equations. This book will be valued by graduate students
and researchers in probability. It can also be used as a textbook for
advanced probability courses.