The book contains a detailed and elementary discussion of Ito integrals and stochastic differential equations. Applications include: Linear filtering theory, diffusion processes, partial differential equations (boundary value problems), optimal stopping, stochastic control. Throughout the text examples are provided to illustrate the content of the results.

Klappentext

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. These 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

Inhalt

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.