科研进展与学术交流报告会 

（第21期）

报告人一： 陈楚楚 副研究员（计算数学与科学工程计算研究所）    

题 目 一：Central limit theorem for approximating ergodic limit of SPDEs via a full discretization  

摘 要 一：The approximation of ergodic limit is of fundamental importance in many applications. In this talk, we focus on characterizing quantitatively the fluctuations between the ergodic limit and the time-averaging estimator of the full discretization for the parabolic stochastic partial differential equation. We establish a central limit theorem, which shows that the normalized time-averaging estimator converges to a normal distribution with the variance being the same as that of the continuous case, where the scale used for the normalization corresponds to the temporal strong convergence rate of the considered full discretization.  

报告人二： 赵国焕 副研究员（应用数学研究所）    

题 目 二：Non-local operators with low-order singular kernels  

摘 要 二: The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-local operators generated by L vy processes with low-intensity small jumps (for instance $\log(1-\Delta)$) is unclear. 

In this talk, I will first briefly introduce the Markov processes and operators satisfying the positive maximal principle, especially pure jump processes and non-local operators. After that, I plan to present some regularity results for non-local operators with critically low singularity kernels that do not allow standard scaling. For instance, Schauder-type estimates for log Laplacian operators and operators generated by geometric stable processes will be discussed. To obtain desired conclusions, a new notion of Hoelder spaces (depending on the operators) will be introduced, and some probabilistic methods will be shown to overcome technical difficulties. In turn, I will also show how the analytic results can be applied to stochastic analysis.  

时  间：2023.1.3(星期五), 10:40-13:00    

地  点：腾讯会议671-4985-6447    

报告会视频