Heriot-Watt Mathematics Report Series
HWM10-21, 26 May 2010

A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems

E Buckwar and T Sickenberger


Abstract

We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the Theta-Maruyama and the Theta-Milstein method in this context. We propose a technique, based on the vectorisation of matrices and the Kronecker product, to deal with the matrix expressions arising in this analysis and provide the explicit structure of the stability matrices in the general case of linear systems of SDEs. For a set of simple test SDE systems, incorporating different noise structures but only a few parameters, we apply the general results and provide visual and numerical comparisons of the stability properties of the two methods.

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Full text: http://www.ma.hw.ac.uk/~ts117/publ/Buckwar_Sickenberger_Structural_Analysis_Of_Asym_MS_Stability_For_SDE_Systems.pdf


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