对称α稳态过程驱动的随机微分方程数值分析  

Numerical analysis for stochastic differential equations driven by symmetric α-stable process

作　　者：胡军浩[1] 高帅斌 刘暐[2] HU Junhao;GAO Shuaibin;LIU Wei(College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074 [2]上海师范大学数学系,上海200234

出　　处：《中南民族大学学报（自然科学版）》2020年第4期431-435,共5页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61876192,11701378,11871343,11971316);中南民族大学研究生创新基金项目(3212020sycxjj306)。

摘　　要：研究了一类对称α稳态过程驱动的随机微分方程数值解问题.这类随机微分方程的漂移项具有超线性增长系数.采用半隐式Euler-Maruyama算法得到:对于任意小的ε>0和α∈[1,2),其数值解强收敛率是α-ε4.In this paper,the numerical solution of a class of stochastic differential equations driven by symmetricα-stable process is studied.The drift coefficient of stochastic differential equations under consideration is allowed to grow super-linearly.The strong convergence of numerical solution by the semi-implicit Euler-Maruyama algorithm is shown with the rate ofα-ε4 for arbitrarily smallε>0 andα∈[1,2).

关 键 词：随机微分方程 对称α稳态过程 半隐式Euler-Maruyama算法 强收敛率 

分 类 号：O241.8[理学—计算数学]