Stochastic Differential Equations An Introduction with Applications

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 presen­ tation is based on some background in measure theory. There are several reasons why one should l...

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Bibliographic Details
Main Author: Oksendal, Bernt
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1985, 1985
Edition:1st ed. 1985
Series:Universitext
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Stochastic Differential Equations  |h Elektronische Ressource  |b An Introduction with Applications  |c by Bernt Oksendal 
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505 0 |a 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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520 |a 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 presen­ 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