We review recent advances in Stein's method and the related stochastic approximation theory in the following three aspects: Advancing stable law approximations via Stein's method, with explicit error bounds for systems exhibiting heavy-tailed behavior; 2) Establishing a new Stein's method for diffusion approximation, which enables a tractable steady-state analysis of queueing systems through approximations of stationary measures for stochastic differential equations. 3) Establishing a unified Markovian framework for stochastic approximations of stochastic optimization algorithms—including SGD, SVRG, and momentum-based variants—to enable comparative analysis of their convergence dynamics.

报告人简介：Dr. Lihu Xu received his Ph.D. from Imperial College London in 2008 and is currently an Associate Professor at the University of Macau (UM), where he has been since 2014. Prior to joining UM, he held postdoctoral research positions at the University of Bonn, Eindhoven University of Technology, and Technische Universität Berlin (2008–2011). From 2011 to 2013, he served as a Lecturer (a permanent role equivalent to Assistant Professor) at Brunel University London. From 09/2011 to 12/2011, Dr. Xu was a visiting scholar at Boston College. From 01/2024 to 07/2024, he was a visiting faculty in the Department of Statistics at Harvard University. Dr. Xu’s research focuses on applied probability and its interdisciplinary applications in theoretical statistics. His work spans Stein's method, stochastic approximations, large deviations, Malliavin calculus, and robust statistical estimation. He has authored over 50 peer-reviewed publications in international journals such as Annals of Applied Probability, Annals of Statistics, Bernoulli, Journal of Functional Analysis, and Probability Theory and Related Fields.