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

Authors:
A. Valinejad;S. Mohammad Hosseini
Affiliations:
Department of Mathematics, Tarbiat Modares University, Tehran, Iran;Department of Mathematics, Tarbiat Modares University, Tehran, Iran
Venue:
Numerical Algorithms
Year:
2010

Citing 12
Cited 2

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On the stability of some second order numerical methods for weak approximation of Itô SDEs

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A stepsize control algorithm for SDEs with small noise based on stochastic Runge---Kutta Maruyama methods

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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.