<電子ブック>
Stochastic Differential Equations : An Introduction with Applications

責任表示
著者
本文言語
出版者
出版年
出版地
関連情報
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
本文を見る Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

詳細

レコードID
主題
SSID
eISBN
登録日 2020.06.27
更新日 2020.06.28