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Zbl 1141.65006
Pang, Sulin; Deng, Feiqi; Mao, Xuerong
Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations. (English)
[J] J. Comput. Appl. Math. 213, No. 1, 127-141 (2008). ISSN 0377-0427

Hybrid stochastic differential systems are designed to model the switching between different systems according to an independent Markov chain. The long time dynamics of numerical approximations of these systems is investigated. Euler-Maruyama discretizations are shown to capture almost sure and moment exponential stability for all sufficiently small time steps under appropriate conditions.
[Dominique Lepingle (Orléans)]

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations
34F05 ODE with randomness
65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: Brownian motion; Euler-Maruyama method; Markov chain; exponential stability; hybrid stochastic differential systems; long time dynamics

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