Evelyn Buckwar [Homepage] and Thorsten Sickenberger [Homepage] Software (MATLAB® files) for
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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. | |
Keywords |
Asymptotic mean-square stability • Theta-Maruyama method • Theta-Milstein method • Systems of stochastic differential equations •
LLinear stability analysis | |
Software download |
You can test the asymptotic mean-square stability of your own d-dimensional linear system of SDEs having m multiplicative noise sources. Download the following files
and insert your drift and diffusion matrices (see the "else" part of the first loop in the main file). Alternatively you can run the test SDE systems of our paper. • main_stability.m - main program file (MATLAB^{®}), defines test-equations and writes outputs • stabanalysis.m - function file (MATLAB^{®}), analysis the system and computes the asymptotic mean-square stability of the zero solution • stabcalculation.m - function file (MATLAB^{®}), computes the asymptotic mean-square stability of Theta-Maruyama and Theta-Milstein approximations for different values of the step-size and the method parameter Theta. | |
Remark |
You might be also interested in A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods (by Evelyn Buckwar and Thorsten Sickenberger), Heriot-Watt Mathematics Report HWM09-13, 2009. | |
Contact |
• Evelyn Buckwar [Homepage] e-mail: e.buckwar@hw.ac.uk • Thorsten Sickenberger [Homepage] e-mail: t.sickenberger@hw.ac.uk | |
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