Seminar by Professor Lihu XU, Department of Mathematics, University of Macau

We review recent advances in Stein's method and the related stochastic approximation theory in the following three aspects: 1) 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.

Lihu Xu currently is an associate professor at the Department of Mathematics, University of Macau. He obtained the PhD in Mathematics from the Imperial College London in 2008, and joined the University of Macau in 2014. His research areas are across the fields of probability, statistics and data science.