کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639568 | 1341239 | 2012 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Exponential mean square stability of numerical methods for systems of stochastic differential equations Exponential mean square stability of numerical methods for systems of stochastic differential equations](/preview/png/4639568.png)
This paper is concerned with exponential mean square stability of the classical stochastic theta method and the so called split-step theta method for stochastic systems. First, we consider linear autonomous systems. Under a sufficient and necessary condition for exponential mean square stability of the exact solution, it is proved that the two classes of theta methods with θ≥0.5θ≥0.5 are exponentially mean square stable for all positive step sizes and the methods with θ<0.5θ<0.5 are stable for some small step sizes. Then, we study the stability of the methods for nonlinear non-autonomous systems. Under a coupled condition on the drift and diffusion coefficients, it is proved that the split-step theta method with θ>0.5θ>0.5 still unconditionally preserves the exponential mean square stability of the underlying systems, but the stochastic theta method does not have this property. Finally, we consider stochastic differential equations with jumps. Some similar results are derived.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 16, October 2012, Pages 4016–4026