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
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 1 2 ，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。
Abstract: 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 1 2 has 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.
文章引用：王晔, 郭平, 贾宏恩, 程岩. 带跳的随机时滞微分方程的截断EM格式的收敛性分析[J]. 应用数学进展, 2024, 13(12): 5393-5405. https://doi.org/10.12677/aam.2024.1312521

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