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An analytic approximation of solutions of stochastic differential delay equations with Markovian switching. (English) Zbl 1185.65009
Summary: We are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory’s approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the \(L^p\)-norm when the drift and diffusion coefficients are Taylor approximations.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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