オクセンダール確率偏微分方程式：モデリング、ホワイトノイズ・アプローチ（テキスト・第２版） Stochastic Partial Differential Equations : A Modeling, White Noise Approach (Universitext) （2ND）

Holden, Helge / Oksendal, Bernt/ Uboe, Jan

Springer（2009/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 325 p.／サイズ 17 illus.
• 商品コード 9780387894874

基本説明

In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise, and introduce new applications of the field.

Full Description

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Levy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.

Contents

Preface to the Second Edition.- Preface to the First Edition.- Introduction.- Framework.- Applications to stochastic ordinary differential equations.- Stochastic partial differential equations driven by Brownian white noise.- Stochastic partial differential equations driven by Lévy white noise.- Appendix A. The Bochner-Minlos theorem.- Appendix B. Stochastic calculus based on Brownian motion.- Appendix C. Properties of Hermite polynomials.- Appendix D. Independence of bases in Wick products.- Appendix E. Stochastic calculus based on Lévy processes- References.- List of frequently used notation and symbols.- Index.