非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析

STRONG CONVERGENCE ANALYSIS OF JUMP-ADAPTED BACKWARD EULER METHOD UNDER NON-GLOBALLY LIPSCHITZ CONDITION

本文研究跳适应向后Euler方法求解跳扩散随机微分方程在非全局Lipschitz条件下的强收敛性.通过克服方程非全局Lipschitz系数给收敛性分析带来的主要困难,我们成功地建立了跳适应后向Euler方法的强收敛性结果并得到相应的收敛率.最后,我们通过数值试验对前文所得理论结果做进一步的验证.

In this paper,we study the strong convergence of jump-adapted backward Euler method for jump-diffusion stochastic differential equations under non-globally Lipschitz condition.By overcoming the main difficulty in the convergence analysis caused by the non-globally Lipschitz coefficients of the the considered problem,we successfully establish the strong convergence result for the jump-adapted backward Euler method with explicit convergence rate identified.Numerical experiments are carried out to confirm our theoretical findings.