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Approximate solutions of stochastic differential delay equations with Markovian switching. (English) Zbl 1098.65005
The Euler-Maruyama method is applied to the approximation of these equations where the coefficients depend on the evolution of an independent finite state space Markov chain. Mean square convergence with order 1/2 is obtained under a global Lipschitz condition. Under a local Lipschitz and linear growth (or bounded moment) condition, mean square convergence still holds true. Under a local Lipschitz condition and an additional Lyapunov condition, convergence in probability is proved. Application is given to stochastic delay Lotka-Volterra equations with Markovian switching.

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)
65C40 Numerical analysis or methods applied to Markov chains
65L20 Stability and convergence of numerical methods for ordinary differential equations
60J65 Brownian motion
60J22 Computational methods in Markov chains
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