Numerical solutions of regime-switching functional diffusions with infinite delay

Abstract

We study a class of diffusion processes which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t). Under suitable conditions, we adopt Euler-Maruyama method to deal with the convergence of numerical solutions of the corresponding stochastic differential equations. More precisely, we investigate convergence rates in the L 2-norm the stochastic functional differential equation with infinite memory and random switching under the global Lipschitz conditions. Then we also discuss L 2-convergence under the local Lipschitz conditions.