Stochastic Flows and Stochastic Differential Equations (Cambridge Studies in Advanced Mathematics) 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Hiroshi Kunita 作者

Cambridge University Press

译者

1997-04-28 出版日期

364 页数

USD 70.00 价格

Paperback

Cambridge Studies in Advanced Mathematics 丛书系列

9780521599252 图书编码

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The 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. Ito 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 Ito'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 Ito'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 given stochastic differential equation define stochastic flows of diffeomorphisms. Some applications are given of particular cases. Chapter 5 is devoted to limit theorems involving stochastic flows, and the book ends with a treatment of stochastic partial differential equations through the theory of stochastic flows. Applications to filtering theory are discussed.

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