2026年随机计算及相关领域前沿进展暑期学校系列学术报告 | Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations
报 告 人: 李晓月
所在单位: 天津工业大学
报告地点: 吉林大学正新楼106
报告时间: 2026-07-18 16:00:00
报告简介:

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

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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。