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Exponential stability of numerical solutions to SDDEs with Markovian switching. (English) Zbl 1105.65010

The authors prove the exponential stability of the Euler method for autonomous stochastic delay differential equations (SDDEs) with Markovian switching the trivial solution of which is exponentially stable in mean square sense.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
34K50 Stochastic functional-differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

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