一类带共同噪声和Lévy过程驱动的McKean-Vlasov随机微分方程的数值分析  

Numerical analysis for a class of McKean-Vlasov stochastic differential equations driven by common noise and Lévy processes

作　　者：胡军浩[1] 刘虎 高帅斌 HU Junhao;LIU Hu;GAO Shuaibin(School of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报(自然科学版)》2025年第2期269-276,共8页Journal of South-Central Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(62373383)。

摘　　要：研究了一类带共同噪声和Lévy过程驱动的McKean-Vlasov随机微分方程的数值方法,其中方程系数满足超线性增长条件.对相应的交互粒子系统构造了自适应Euler-Maruyama算法,并给出了该数值算法的收敛速率.The numerical scheme for a class of McKean-Vlasov stochastic differential equations driven by common noise and Lévy processes is studied,whose coefficients satisfy the superlinear growth condition.The adaptive Euler-Maruyama scheme is constructed for the corresponding interacting particle system,and its convergence rate is shown.

关 键 词：McKean-Vlasov随机微分方程 共同噪声 自适应Euler-Maruyama算法 Lévy过程 

分 类 号：O241.8[理学—计算数学]