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

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.