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Stochastic Differential Equations : An Introduction with Applications

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概要 These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the pres...en tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) 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? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.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
VIII. Applications to Partial Differential Equations
IX. Application to Optimal Stopping
X. Application to Stochastic Control
Appendix A: Normal Random Variables
Appendix B: Conditional Expectations
List of Frequently Used Notation and Symbols.
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登録日 2020.06.27
更新日 2020.06.28