题目：L^2-Exponential ergodicity for stochastic Hamiltonian systems with stable Levy noises
报告人：鲍建海 天津大学 教授
时间: 01月06日（周六）上午10: 40-11: 30
地点：X30456
摘要：Based on the hypocoercivity approach due to Villani, Dolbeault, Mouhot and Schmeiser (TAMS’15) established a new and simple framework to investigate directly the L^2-Exponentialconvergence to the equilibrium for the solution to the kinetic Fokker-Planck equation. Nowadays, the general framework advanced due to Dolbeault, Mouhot and Schmeiser (TAMS’15) is named as the DMS framework for hypocoercivity. Subsequently, Grothaus (JFA’14) builded a dual version of the DMS framework in the kinetic Fokker-Planck setting. No matter what the abstract DMS framework and the dual counterpart due to Grothaus (JFA’14), the densely defined linear operator involved is assumed to be decomposed into two parts, where one part is symmetric and the other part is anti-symmetric.Thus, the existing DMS framework is not applicable to investigate the L^2-Exponentialergodicity for stochastic Hamiltonian systems with stable Levy noises, where one part of the associated infinitesimal generators is anti-symmetric whereas the other part is not symmetric. In this paper, we shall develop a dual version of the DMS framework in the fractional kinetic Fokker-Planck setup, where one part of the densely defined linear operator under consideration need not to be symmetric. As a direct application, we explore the L^2-Exponentialergodicity of stochastic Hamiltonian systems with stable Levy noises. The proof is also based on Poincare inequalities for non-local stable-like Dirichlet forms and the potential theory for fractional Riesz potentials.
个人简介：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学院工作。
主办：西南交通大学研究生院
承办：西南交通大学数学学院、数学中心
