随机微分方程依分布周期解的有限元近似  

Finite Element Approximation to Periodic Solution in Distribution of Stochastic Differential Equation

作　　者：杨雪[1] 胡庆婉 周锦慧 YANG Xue;HU Qingwan;ZHOU Jinhui(College of Mathematics,Jilin University,Changchun 130012,China;School of Mathematics and Statistics,Qujing Normal University,Qujing 655011,Yunnan Province,China)

机构地区：[1]吉林大学数学学院,长春130012 [2]曲靖师范学院数学与统计学院,云南曲靖655011

出　　处：《吉林大学学报（理学版）》2022年第6期1301-1307,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12171199);吉林省科技厅重点项目(批准号:20210201015GX);吉林省科技发展计划项目(批准号:20210201078GX)。

摘　　要：用有限元法求解具有周期性质的概率密度函数研究其随机周期解的统计性质,证明全空间近似解的积分守恒性以及截断到有限区间上近似解的空间积分近似守恒性,并通过数值实例验证方法的有效性.The finite element method was used to solve the probability density function with periodic properties to study the statistical properties of stochastic periodic solutions. We proved the integral conservation of the full space approximate solution and the spatial integral approximate conservation of the approximate solution truncated to a finite interval, and verified the effectiveness of the method by numerical experiments.

关 键 词：随机微分方程 依分布随机周期解 FOKKER-PLANCK方程 有限元方法 近似守恒性 

分 类 号：O242.21[理学—计算数学]