报告人：曾才斌（华南理工大学）

报告题目：Random Attractors and Invariant Manifolds for SPDEs with fBm

报告摘要：Different from Brownian motion, fractional Brownian motion (fBm) is neither Markovian nor a semi-martingale. Little seems to be known about the long-time behavior of systems with an fBm. In this respect, we shall report two recent results. First, we establish the existence of random attractors for SPDEs driven by rough path with Hölder index in (1/3, 1/2] by combining rough paths theory and stopping times analysis in a scale of interpolation spaces. Second, we analyze the Lu-Schmalfuß conjecture on the existence of stable manifolds for SPDEs with nonlinear multiplicative fractional noise. To this aim, we construct a function space in which the discretized Lyapunov-Perron-type operator has a unique fixed point. The two papers are written in collaboration with Qigui Yang, Xiaofang Lin and Alexandra Neamţu.

报告时间：2024年6月2日（星期日）10:30-12:00

报告地点：科技楼南706会议室

邀请人：李骥

报告人简介：曾才斌，华南理工大学教授、博士生导师、统计与金融数学系副主任，研究方向为随机微分动力系统，在JFA、JDE等学术期刊发表论文40余篇，主持承担了2项国家自然科学基金面上项目、1项国家自然科学基金天元讲习班项目、国家自然科学基金青年项目、5项省部级项目，先后学术访问犹他州立大学、赫尔辛基大学、杨百翰大学，曾获广东省优秀博士学位论文称号。