Numerical solutions of SDEs with Markovian switching and jumps under non-Lipschitz conditions

Abstract

In this paper the numerical solutions to stochastic differential equations with Markovian switching and jumps under non-Lipschitz conditions are considered. Firstly, we study the existence and uniqueness of solutions to this class of equations. Then we present the moment bounds of the exact and numerical solutions. It is also proved that the strong rate of convergence of the Euler scheme is equal to 1 ∕ 2 with the drift coefficient satisfying one-sided Lipschitz condition while the diffusion and jump coefficients satisfy global Lipschitz conditions. Some numerical examples are given to confirm the theoretical results.