报告题目： Limit Theorems for Numerical Methods of SPDEs

报告人：周滔 讲师

报告时间：2026年7月20日 14:30-15:30

报告地点：数学与统计学院210会议室

邀请人：曾莉

邀请单位：福州大学数学与统计学院

报告摘要：This report presents some advances in the limit theorems for numerical methods of stochastic partial differential equations (SPDEs). For parabolic SPDEs, we investigate the asymptotic distribution of errors between time-averaged estimators and their ergodic limits, and establish a central limit theorem for numerical solutions. Adopting the optimal strong convergence rate as the normalization factor, the obtained results enable the construction of confidence intervals and the evaluation of computational costs. For stochastic wave equations with non-globally Lipschitz dissipative damping, we construct appropriate Lyapunov functionals to prove exponential ergodicity and derive error estimates for invariant measures under the Wasserstein distance and in the weak topology. Furthermore, strong laws of large numbers are established for both exact and numerical solutions, which verify the almost sure convergence of time averages to the corresponding ergodic limits.

报告人简介：周滔，现任湖南师范大学数学与统计学院讲师。 2018年本科毕业于湖南师范大学数学与统计学院，2023年博士毕业于中国科学院数学与系统科学研究院计算数学与科学工程计算研究所。主要从事随机微分方程分析与计算方面的研究工作，研究成果发表在 IMA J. Numer. Anal., J. Comput. Phys., ESAIM Math. Model. Numer. Anal., Stochastic Process. Appl., Stoch. Partial Differ. Equ. Anal. Comput., Front. Math.等期刊。

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