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Stochastic Differential Equations : An Introduction with Applications
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| 概要 | From the reviews to the first edition: Most of the literature about stochastic differential equations seems to place so much emphasis on rigor and completeness that it scares the nonexperts away. Thes...e notes are an attempt to approach the subject from the nonexpert point of view.: Not knowing anything ... about a subject to start with, what would I like to know first of all. My answer would be: 1) In what situations does the subject arise ? 2) What are its essential features? 3) What are the applications and the connections to other fields?" The author, a lucid mind with a fine pedagocical instinct, has written a splendid text that achieves his aims set forward above. He starts out by stating six problems in the introduction in which stochastic differential equations 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 thetheory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respectto Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications"... It 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. From: Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986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/2324/1000034457 |
| 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 |