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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.
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登録日 2020.06.27
更新日 2020.06.28