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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:
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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