A variable step-size control algorithm for the weak approximation of stochastic differential equations

A variable step-size control algorithm for the weak approximation of stochastic differential equations

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Article ID: iaor20108159
Volume: 55
Issue: 4
Start Page Number: 429
End Page Number: 446
Publication Date: Dec 2010
Journal: Numerical Algorithms
Authors: ,
Abstract:

In this paper, we propose two local error estimates based on drift and diffusion terms of the stochastic differential equations in order to determine the optimal step-size for the next stage in an adaptive variable step-size algorithm. These local error estimates are based on the weak approximation solution of stochastic differential equations with one-dimensional and multi-dimensional Wiener processes. Numerical experiments are presented to illustrate the effectiveness of this approach in the weak approximation of several standard test problems including SDEs with small noise and scalar and multi-dimensional Wiener processes.

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