Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

Xu Yang; Weidong Zhao

doi:10.4208/aamm.2015.m1208

Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

Authors

Xu Yang
Weidong Zhao

DOI:

https://doi.org/10.4208/aamm.2015.m1208

Keywords:

Split-step scheme, strong convergence, stochastic differential equation, jump-diffusion, one-side Lipschitz condition.

Abstract

In this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.