报告题目：Approximation of heavy-tailed distribution via stable-driven SDEs

报告人：黄璐静

单位：福建师范大学

时间：2022年12月28日09:00-11:00

腾讯会议：642-870-386

摘要：Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differential equations (SDEs) driven by the Brownian motion. However, for some heavy-tailed distributions it can be shown that the associated SDE is not exponentially ergodic and that related sampling algorithms may perform poorly. A natural idea that has recently been explored in the machine learning literature in this context is to make use of stochastic processes with heavy tails instead of the Brownian motion. In this paper, we provide a rigorous theoretical framework for studying the problem of approximating heavy-tailed distributions via ergodic SDEs driven by symmetric (rotationally invariant)α-stable processes. Based on joint work with Mateusz B. Majka and Jian Wang.

简介:黄璐静，福建师范大学数学与统计学院副教授。2018年博士毕业于北京师范大学，主要研究方向为马氏过程遍历性，现主持国家自然科学基金青年项目一项。