Simulation of space and space-time bounded diffusions
“Ordinary” mean-square methods from Chap. 1, intended to solve SDEs on a finite time interval, are based on a time discretization (sampling). The space-time point, corresponding to an “ordinary” one-step approximation constructed at a time point tk, lies
- PDF / 46,143,637 Bytes
- 612 Pages / 439.37 x 666.142 pts Page_size
- 6 Downloads / 155 Views
Springer-Verlag Berlin Heidelberg GmbH
G. N. Milstein M. V. Tretyakov
Stochastic Numerics for Mathematical Physics With 48 Figures and 28 Tables
,
Springer
Professor Grigori N. Milstein Weierstrass Institute for Applied Analysis and Stochastics Mohrenstrasse 39 10117 Berlin, Germany and Ural State University Department of Mathematics Lenin Str. 51 620083 Ekaterinburg, Russia
Dr. Michael V. Tretyakov University of Leicester Department of Mathematics Leicester LEI 7RH United Kingdom
Library of Congress Control Number:
2004103618
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 978-3-642-05930-8
ISBN 978-3-662-10063-9 (eBook)
DOI 10.1007/978-3-662-10063-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law ofSeptember 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin HeideIberg GmbH. Violations are liable to prosecution under the German Copyright Law.
springeronline.com © Springer-Verlag Berlin Heidelberg 2004
Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover Ist edition 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data prepared by the authors using a Springer TsJ( macro package Production: PTP-Berlin Protago-TeX-Production GmbH, Germany Cover design: design 6- production GmbH, Heidelberg Printed on acid-free paper 55/3141/YU 5 4 3 2 1 o
Preface
Using stochastic differential equations (SDEs), we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory, signal processing and filtering, physics, biology and chemistry, economics and finance, to mention just a few. However the very importance acquired by SDEs lies, to a large extent, in the strong connection they have with the equations of mathematical physics. It is well known that problems of mathematical physics involve "damned dimensions" , often leading to severe difficulties in solving boundary value problems. A way out is provided by the employment of probabilistic representations together with Monte Carlo methods. As a result, a complex multi-dimensional problem for partial differential equations (PDEs) reduces to the Cauchy problem for a system of SDEs. The last system can naturally be
