Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations
报告人:李晓月
报告地点:人民大街校区数学与统计学院二楼会议室
报告时间:2026年07月28日星期二10:40-11:30
邀请人:冀书关
报告摘要:
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with super-linear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense. The optimal uniform-in-time strong convergence rate $1/2$-order of the numerical solutions is obtained for the interacting particle system. Furthermore, it is proved that the numerical solutions capture the long-term dynamical behaviors of MV-SDEs precisely, including moment boundedness, stability, and ergodicity. Moreover, a unique numerical invariant probability measure is yielded, which converges to the underlying invariant probability measure of MV-SDEs in the $L^2$-Wasserstein distance. Finally, several numerical experiments are carried out to support the main results.
主讲人简介:
李晓月,天津工业大学数学科学学院教授,博士生导师。现任天津工业大学数学科学学院常务副院长,兼任中国数学会理事、天津市数学学会副理事长、天津市工业与应用数学学会常务理事。长期从事非线性随机微分方程动力学理论及其数值逼近理论的研究,在SIAMJ.Numer.Anal.,Math.Comp.,JDE,SPA等期刊上发表论文50余篇,主持国家自然科学基金面上项目3项以及多项省部级项目的研究工作。