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Authorร{152}ksendal, Bernt. author
TitleStochastic Differential Equations [electronic resource] : An Introduction with Applications / by Bernt ร{152}ksendal
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992
Edition Third Edition
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Descript XIII, 228 p. 3 illus. online resource


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


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

Mathematics Mathematical analysis Analysis (Mathematics) System theory Calculus of variations Probabilities Mathematics Probability Theory and Stochastic Processes Systems Theory Control Calculus of Variations and Optimal Control; Optimization Analysis


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