Strong convergence of compensated split-step theta methods for SDEs with jumps under monotone condition

Abstract

This paper is concerned with strong convergence of the compensated split-step theta (CSST) method for autonomous stochastic differential equations (SDEs) with jumps under weaker conditions. More precisely, the diffusion coefficient and the drift coefficient are both locally Lipschitz and the jump-diffusion coefficient is globally Lipschitz, while they all satisfy the monotone condition. It is proved that the CSST method is strongly convergent of order 12. Finally, the obtained results are supported by numerical experiments.