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Stochastic Flows and Stochastic Differential Equations

Stochastic Flows and Stochastic Differential Equations

£57.00

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 1997
  • availability: Available
  • format: Paperback
  • isbn: 9780521599252

£ 57.00
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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. Itô 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 Itô'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 Itô'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.

    • Excellent author
    • HB has sales in excess of 1000
    • Can be used for advanced courses or for self study
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    Product details

    • Date Published: April 1997
    • format: Paperback
    • isbn: 9780521599252
    • length: 364 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.53kg
    • availability: Available
  • Table of Contents

    1. 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.

  • Author

    Hiroshi Kunita, Kyushu University, Japan

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