带跳的随机时滞微分方程的截断EM格式的收敛性分析  

The Convergence of the Truncated Euler-Maruyama Method for Stochastic Delay Differential Equations with Poisson Jumps

作　　者：王晔 郭平 贾宏恩 程岩 

机构地区：[1]太原理工大学数学学院,山西 太原

出　　处：《应用数学进展》2024年第12期5393-5405,共13页Advances in Applied Mathematics

基　　金：国家自然科学基金(No. 12301521),山西省自然科学基金(No. 20210302124081, No. 202303021211026),山西省留学归国人员资助项目(No.2023-038)。

摘　　要：本文证明了带泊松跳的随机时滞微分方程的截断EM格式的收敛性。通过讨论截断EM格式的随机C-稳定性和随机B相容性,研究了数值格式的收敛性及其收敛阶为12,从而避免了讨论数值解高阶矩的有界性。最后,通过一个例子说明了截断EM格式对带泊松跳的SDDEs的收敛性与理论结果的一致性。The convergence of the truncated Euler-Maruyama (EM) method for the stochastic delay differential equations (SDDEs) with poisson jumps are established in this paper. By discussing the stochastic C-stability and stochastic B-consistency of the truncated EM scheme, the convergence and convergence rate which is 12has been researched, which avoiding the explore of the boundedness of the high-order moments of the numerical solution. Finally, an example is given to illustrate the consistence with the theoretical results on the convergence of the truncated EM to the SDDEs with poisson jumps.

关 键 词：随机时滞微分方程 泊松跳 截断EM格式 随机C稳定性 随机B相容性 

分 类 号：O17[理学—数学]