| 非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析 |
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| 引用本文： | 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. |
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| 作者姓名： | 杨旭 赵卫东 |
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| 作者单位： | 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 |
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| 基金项目： | 国家重点研发计划;国家自然科学基金 |
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| 摘 要： | 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.
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| 关 键 词： | 跳适应方法 跳扩散问题 Poisson跳 强收敛率 非全局Lipschitz系数 |
| 收稿时间： | 2020-11-26 |
STRONG CONVERGENCE ANALYSIS OF JUMP-ADAPTED BACKWARD EULER METHOD UNDER NON-GLOBALLY LIPSCHITZ CONDITION |
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| 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. |
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| Authors: | Yang Xu Zhao Weidong |
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| Institution: | 1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;2. School of Mathematics, Shandong University, Jinan 250100, China |
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| Abstract: | 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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| Keywords: | jump-adapted method jump-diffusion problem Poisson jumps strong convergence rate non-Lipschitz coefficient |
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