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Stochastic Differential Equations : An Introduction with Applications
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| 概要 | From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential eq...uations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2続きを見る |
| 目次 | I. Introduction II. Some Mathematical Preliminaries III. Ito Integrals IV. Stochastic Integrals and the Ito Formula V. Stochastic Differential Equations VI. The Filtering Problem VII. Diffusions: Basic Properties VIII. Other Topics in Diffusion Theory IX. Applications to Boundary Value Problems X. Application to Optimal Stopping XI. Application to Stochastic Control Appendix A: Normal Random Variables Appendix B: Conditional Expectations Appendix C: Uniform Integrability and Martingale Convergence List of Frequently Used Notation and Symbols.続きを見る |
| 冊子版へのリンク | http://hdl.handle.net/2324/1001385515 |
| 本文を見る | Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive) |
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| 登録日 | 2020.06.27 |
| 更新日 | 2020.06.28 |