Convergence of the compensated split-step θ-method for nonlinear jump-diffusion systems.

In this paper, our aim is to develop a compensated split-step θ (CSS θ) method for nonlinear jump-diffusion systems. First, we prove the convergence of the proposed method under a one-sided Lipschitz condition on the drift coefficient, and global Lipschitz condition on the diffusion and jump coefficients. Then we further show that the optimal strong convergence rate of CSS θ can be recovered, if the drift coefficient satisfies a polynomial growth condition. At last, a nonlinear test equation is simulated to verify the results obtained from theory. The results show that the CSS θ method is efficient for simulating the nonlinear jump-diffusion systems. [ABSTRACT FROM AUTHOR]