Convergence and stability of the balanced methods for stochastic differential equations with jumps

Abstract

This paper deals with the balanced methods which are implicit methods for stochastic differential equations with Poisson-driven jumps. It is shown that the balanced methods give a strong convergence rate of at least 1/2 and can preserve the linear mean-square stability with the sufficiently small stepsize. Weak variants are also considered and their mean-square stability analysed. Some numerical experiments are given to demonstrate the conclusions.