Stochastic Differential Equations
This book gives an introduction to the basic theory of shastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often...
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This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010. Booknews This typographically unaesthetic (because typed) but otherwise very attractive text (corrected and somewhat revised from the edition of 1985) derives from a course for undergraduates which the author (University of Oslo) presented at Edinburgh University in 1982. His objective is to communicate to non-experts a sense of the domain of applications to which the theory of stochastic differential equations most naturally applies, and of the principal components of that theory. In the introductory chapter he poses six illustrative problems, which serve to motivate the theoretical developments (presented sometimes only in outline) which are the subject matter of the succeeding ten chapters. He provides numerous examples but (oddly) no exercises. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
1Introduction12Some Mathematical Preliminaries73Ito Integrals214The Ito Formula and the Martingale Representation Theorem435Stochastic Differential Equations636The Filtering Problem837Diffusions: Basic Properties1138Other Topics in Diffusion Theory1399Applications to Boundary Value Problems17510Application to Optimal Stopping20511Application to Stochastic Control23512Application to Mathematical Finance261App. ANormal Random Variables305App. BConditional Expectation309App. CUniform Integrability and Martingale Convergence311App. DAn Approximation Result315Solutions and Additional Hints to Some of the Exercises319References345List of Frequently Used Notation and Symbols353Index357
