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Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations. (English) Zbl 1141.65006
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.
MSC:
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
60H35Computational methods for stochastic equations
34F05ODE with randomness
65L06Multistep, Runge-Kutta, and extrapolation methods
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