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Convergence and stability of numerical solutions to SDDEs with Markovian switching. (English) Zbl 1095.65005

The authors consider the numerical solution of stochastic delay differential equations (SDDEs) that are influenced by Markov switching processes. It clarifies the numerical stability and strong convergence of the Euler method.

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)
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

[1] Mao, X.; Matasov, A.; Piunovskiy, A. B., Stochastic differential delay equations with Markovian switching[J], Bernoulli, 6, 1, 73-90 (2000) · Zbl 0956.60060
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[13] Cao, W.; Liu, M.; Fan, Z., MS-stability of the Euler-Maruyama method for stochastic differential delay equations[J], J. Appl. Math. Comput., 159, 127-135 (2004) · Zbl 1074.65007
[14] Yuan, C.; Mao, X., Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching[J], Math. Comput. Simul., 64, 223-235 (2004) · Zbl 1044.65007
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