Overview

This text is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book should be of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Full Product Details

Author:   G.N. Milstein
Publisher:   Springer
Imprint:   Springer
Edition:   1995 ed.
Volume:   313
Dimensions:   Width: 15.60cm , Height: 1.20cm , Length: 23.40cm
Weight:   0.970kg
ISBN:  

9780792332138

ISBN 10:   079233213
Pages:   172
Publication Date:   30 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Mean-square approximation of solutions of systems of stochastic differential equations.- 2. Modeling of Itô integrals.- 3. Weak approximation of solutions of systems of stochastic differential equations.- 4. Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals.

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