带奇异系数的McKean-Vlasov方程的弱解  

The weak solution of McKean-Vlasov stochastic differential equation with singular coefficients

作　　者：马丽[1] 李钰静 MA Li;LI Yu-jing(Department of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China)

机构地区：[1]海南师范大学数学与统计学院,海南海口571158

出　　处：《东北师大学报（自然科学版）》2023年第3期24-29,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金(地区基金)资助项目(11861029);海南省高层次人才基金资助项目(120RC589);海南省研究生创新科研课题项目(Hys2020-325);海南省院士创新平台科研项目(YSPTZX202215).

摘　　要：研究了分布依赖的随机微分方程弱解的存在性问题,得到弱解的存在性及一些估计.由弱解的估计及Prohov定理得到解的分布序列是胎紧的,再由Skorohod表示定理得到分布序列的极限,并对递推定义的方程两侧取极限得到弱解的存在性.The existence of weak solutions for distribution dependent stochastic differential equations is studied.By the estimation of weak solutions and Prohov theorem,it is proved that the distribution sequence of solutions is tight and get the limit of distribution sequence by Skorohod representation theorem.The existence of weak solution is given by taking the limit on both sides of the recursively defined equation and proving the convergence of each term.

关 键 词：分布依赖的随机微分方程 系数退化 弱解存在性 

分 类 号：O211.63[理学—概率论与数理统计]