报告题目：On the Exponential Ergodicity and Large Deviations of Stochastic Hessian-Driven Damping Hamiltonian Systems

报 告 人：蒋继发教授（河南师范大学）

报告时间：2025年4月21日  10:00

报告地点：数学研究中心528

报告摘要：

Stimulated by the invalidation of existing theories to apply to the famous Moser equation, a Hessian-driven damping Hamiltonian systems, this talk will present a new exponential ergodicity and Donsker and Varadhan's large deviation theorem for stochastic Hessian-driven Hamiltonian systems, making it applicable to the Moser equation and many other physical models and the optimization model. We will construct polynomial Lyapunov functions instead of existing exponential Lyapunov functions, which overcome the exponential explosion phenomenon and expand the optimal initial distribution spaee, and have better dynamics, probability and practical significance. Then exponential ergodicity is achieved by the Harris Theorem and the Donsker and Varadhan large deviation is done by Wu's criterion.

报告人简介：

蒋继发，河南师范大学教授，博士生导师，1992年被国家人事部评为有突出贡献的中青年专家，并获国务院政府特殊津贴。曾获安徽省科技进步奖二等奖、华和曾宪梓教育基金奖。培养的两名博士的论文入选全国优秀百篇博士论文，一名博士的论文入选上海市研究生优秀成果。目前的研究方向为随机微分方程和随机动力系统，主要研究成果发表于J. Reine. Angew. Math., SIMA, SIAR, SICON, SIADS, Trans. Amer. Math. Soc., Nonlinearity等。