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非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析

杨旭1, 赵卫东2   

  1. 1. 中国矿业大学数学学院, 徐州 221116;
    2. 山东大学数学学院, 济南 250100
  • 收稿日期:2020-11-26 出版日期:2022-05-14 发布日期:2022-05-06
  • 基金资助:
    国家自然科学基金项目(11901565,12071261,11831010,11871068)和国家重点研发计划项目(2018YFA0703900)资助.

杨旭, 赵卫东. 非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析[J]. 计算数学, 2022, 44(2): 163-177.

Yang Xu, Zhao Weidong. STRONG CONVERGENCE ANALYSIS OF JUMP-ADAPTED BACKWARD EULER METHOD UNDER NON-GLOBALLY LIPSCHITZ CONDITION[J]. Mathematica Numerica Sinica, 2022, 44(2): 163-177.

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

Yang Xu1, Zhao Weidong2   

  1. 1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;
    2. School of Mathematics, Shandong University, Jinan 250100, China
  • Received:2020-11-26 Online:2022-05-14 Published:2022-05-06
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.

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