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：Cramer-type moderate deviation describes the precise asymptotic behavior of tail probabilities of normalized sums in the regime between the central limit theorem and large deviations, and has wide applications in statistical inference, saddlepoint approximation, and resampling methods. In this talk, we first introduce the definition and classical results of Cramér-type moderate deviations for independent random variables.

Next consider an ergodic stochastic differential equation and its Euler–Maruyama (EM) scheme: under appropriate conditions, both admit a unique invariant measure. Based on the empirical measure of the EM scheme as a statistic of the invariant measure, one can establish a self-normalized Cramér-type moderate deviation for the normalized fluctuation around the invariant measure. The result holds in the same range as the classical results.

报告人简介：张凤山，长春大学数学与统计博彩App 副教授。2023年在博彩App 取得博士学位，2023-2025年在中国科博彩App 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. Numer. Anal.》、《J. Sci. Comput.》、《Adv. Comput. Math.》、《Commun. Comput. Phys.》。