报告题目：The Cramer-type moderate deviation for Euler-Maruyama scheme

报告人：张凤山 副教授 长春大学

报告时间：2026年10月15日下午16:00

报告地点：正新楼103

校内联系人：邹永魁 邮箱 [email protected]

报告摘要：For the general time-homogeneous Markov process, do numerical discretizations exactly preserve its probabilistic limit behaviors, in particular the strong LLN and the CLT? This paper gives a positive answer to the question by proposing a unified and transparent approach to investigating probabilistic limit behaviors of numerical discretizations of time-homogeneous Markov processes. Once the properties of uniformly mixing and convergence for numerical discretizations are satisfied, it is shown that the time-averages of numerical discretizations converge to the ergodic limit in the almost surely sense and that the normalized time-averages converge in distribution to a normal distribution. The limits coincide with the ones for the underlying Markov process. Our results have the merit of the flexible application to numerical discretizations for a large class of stochastic differential equations. Notably, the preservation of these probabilistic limit behaviors of the full discretization of the stochastic Allen--Cahn equation and numerical discretizations of stochastic functional differential equations are obtained for the first time.

报告人简介：宋国婷，长春大学数学与统计学院副教授。2022年在东北师范大学取得博士学位，2022-2024年在中国科学院数学与系统科学研究院从事博士后研究工作。研究兴趣聚焦于非线性随机微分方程的数值算法理论，部分成果发表在《SIAM J. Appl. Math.》、《J. Differential Equations》、《Bernoulii》、《Stochastic Process. Appl.》，2026年获批国家自然科学青年基金C类项目。