Numerical Solution of Stochastic Differential Equations / Edition 1

by Peter E. Kloeden, Eckhard Platen

Overview

The aim of this book is to provide an accessible introduction to shastic differential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the development of numerical methods for shastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the reported work has been motivated by the need to solve particular types of problems, for which, even more so than in the deterministic context, specific methods are required. The treatment has often been heuristic and ad hoc in character. Nevertheless, there are underlying principles present in many of the papers, an understanding of which will enable one to develop or apply appropriate numerical schemes for particular problems or classes of problems.

Product Details

ISBN-13:	9783642081071
Publisher:	Springer Berlin Heidelberg
Publication date:	12/01/2010
Series:	Stochastic Modelling and Applied Probability , #23
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	636
Product dimensions:	6.10(w) x 9.20(h) x 1.50(d)

Table of Contents

1. Probability and Statistics.- 2. Probability and Shastic Processes.- 3. Ito Shastic Calculus.- 4. Shastic Differential Equations.- 5. Shastic Taylor Expansions.- 6. Modelling with Shastic Differential Equations.- 7. Applications of Shastic Differential Equations.- 8. Time Discrete Approximation of Deterministic Differential Equations.- 9. Introduction to Shastic Time Discrete Approximation.- 10. Strong Taylor Approximations.- 11. Explicit Strong Approximations.- 12. Implicit Strong Approximations.- 13. Selected Applications of Strong Approximations.- 14. Weak Taylor Approximations.- 15. Explicit and Implicit Weak Approximations.- 16. Variance Reduction Methods.- 17. Selected Applications of Weak Approximations.- Solutions of Exercises.- Bibliographical Notes.

Editorial Reviews

"... the authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible. This was not an easy task... Their exposition stresses clarity, not formality - a very welcome approach." ZAMP

From the Publisher

Provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasizing the numerical methods needed to solve such equations. Serves as a basic text and offers access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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