stochastic differential equations mean-square numerical methods stepsize control small noise Stepsize control for mean-square numerical methods for stochastic differential equations with small noise Werner Römisch Römisch Werner Renate Winkler Winkler Renate Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Stepsize control for mean-square numerical methods for stochastic differential equations with small noise
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Werner Römisch , Renate Winkler

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

65C30 Stochastic differential and integral equations
60-08 Computational methods

Abstract
A strategy for controlling the stepsize in the numerical integration of stochastic differential equations (SDEs) is presented. It is based on estimating the p-th mean of local errors. The strategy leads to deterministic stepsize sequences that are identical for all paths. For the family of Euler schemes for SDEs with small noise we derive computable estimates for the dominating term of the p-th mean of local errors and show that the strategy becomes efficient for reasonable stepsizes. Numerical experience is reported for test examples including scalar SDEs and a stochastic circuit model.

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