报告人：鲍建海教授

报告题目：Geometric ergodicity of modified Euler schemes for SDEs with super-linearity

报告摘要：As a well-known fact, the classical Euler scheme works merely for SDEs with coefficients of linear growth. In this paper, we study a general framework of modified Euler schemes, which is applicable to SDEs with super-linear drifts and encompasses numerical methods such as the tamed Euler scheme and the projected Euler scheme, and investigate the associated long-time asymptotic. In detail, on the one hand, by exploiting an approach based on the refined basic coupling, we show that all Euler recursions within our proposed framework are geometrically ergodic under a mixed probability distance (i.e., the total variation distance plus the L¹-Wasserstein distance) and the weighted total variation distance. On the other hand, by utilizing the coupling by reflection, we demonstrate that the tamed Euler scheme is contractive under the L¹-Wasserstein distance. In addition, as an important application of this contractivity result, we provide a quantitative L¹-Wasserstein error bound between the exact invariant probability measure of an SDE with super-linearity, and the invariant probability measure of the corresponding tamed Euler scheme. Our results substantially extend the current literature, where related results on long-time behavior of Euler schemes have been available only for SDEs with globally Lipschitz coefficients (i.e., coefficients of linear growth).

报告时间：2025年8月25日  9:30-10:30

报告地点：正心楼306

报告人简介：鲍建海，教授，现任职于天津大学应用数学中心。主要从事随机分析等相关领域研究。2013年01月获英国斯旺西大学博士学位；2012年9月-2013年8月在美国韦恩州立大学从事Research Fellow；2017年1月-2019年12月在英国斯旺西大学从事博士后研究；2013年9月-2020年6月，在中南大学数学与统计公司工作。