Higham, D.J. and Mao, X. and Stuart, A.M. (2003) Exponential mean square stability of numerical solutions to stochastic differential equations. LMS Journal of Computation and Mathematics, 6. pp. 297-313. ISSN 1461-1570Full text not available in this repository. (Request a copy from the Strathclyde author)
Positive results are proved here about the ability of numerical simulations to reproduce the exponential mean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step sizes) are shown to be equivalent, and the corresponding second-moment Lyapunov exponent bounds can be taken to be arbitrarily close. The required finite-time convergence conditions hold for the class of stochastic theta methods on globally Lipschitz problems. It is then shown that exponential mean-square stability for non-globally Lipschitz SDEs is not inherited, in general, by numerical methods. However, for a class of SDEs that satisfy a one-sided Lipschitz condition, positive results are obtained for two implicit methods. These results highlight the fact that for long-time simulation on nonlinear SDEs, the choice of numerical method can be crucial.
|Keywords:||stochastic differential equations, numerical simulations, Lipschitz problems, mean-square stability, SDEs, Mathematics, Mathematics(all), Computational Theory and Mathematics|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Ms Sarah Scott|
|Date Deposited:||22 Feb 2006|
|Last modified:||23 Sep 2016 00:03|