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The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations

Published online by Cambridge University Press:  01 February 2010

P.E. Kloeden  and
A. Neuenkirch
P.E. Kloeden
Affiliation:
Johann Wolfgang Goethe-Universität, Institut für Mathematik, Robert-Mayer-Strasse 10, 60325 Frankfurt am Main, Germany, kloeden@math.uni-frankfurt.de, http://www.math.uni-frankfurt.de/~numerik/kloeden/
A. Neuenkirch
Affiliation:
Johann Wolfgang Goethe-Universität, Institut für Mathematik, Robert-Mayer-Strasse 10, 60325 Frankfurt am Main, Germany, neuenkirch@math.uni-frankfurt.de, http://www.math.uni-frankfurt.de/~neuenkir/

Abstract

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The authors of this paper study approximation methods for stochastic differential equations, and point out a simple relation between the order of convergence in the pth mean and the order of convergence in the pathwise sense: Convergence in the pth mean of order α for all p ≥ 1 implies pathwise convergence of order α – ε for arbitrary ε > 0. The authors then apply this result to several one-step and multi-step approximation schemes for stochastic differential equations and stochastic delay differential equations. In addition, they give some numerical examples.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 10 , 2007 , pp. 235 - 253
Copyright
Copyright © London Mathematical Society 2007

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