Approximations of the Euler–Maruyama Method of Stochastic Differential Equations with Regime Switching

This work focuses on a class of regime-switching diffusion processes with both continuous components and discrete components. Under suitable conditions, we adopt the Euler–Maruyama method to deal with the convergence of numerical solutions of the corresponding stochastic differential equations. More precisely, we first show the convergence rates in the Lp-norm of the stochastic differential equations with regime switching under Lipschitz conditions. Then, we also discuss L1 and L2 convergence under non-Lipschitz conditions.