Description
Book SynopsisThe main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows. The classical theory was initiated by K. Ità and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby ItÃ's theory as a special case. The book can be used with advanced courses on probability theory or for self-study. The author begins with a discussion of Markov processes, martingales and Brownian motion, followed by a review of ItÃ's stochastic analysis. The next chapter deals with continuous semimartingales with spatial parameters, in order to study stochastic flow, and a generalisation of Ito's equation. Stochastic flows and their relation with this are generalised and considered in chapter 4. It is shown that solutions of a g
Trade Review"The book could be used with advanced courses on probability theory or for self study." MTW, JASA
Table of Contents1. Stochastic processes and random fields; 2. Continuous semimartingales and stochastic integrals; 3. Semimartingales with spatial parameter and stochastic integrals; 4. Stochastic flows; 5. Convergence of stochastic flows; 6. Stochastic partial differential equations.
