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

报告人：曾才斌教授，华南理工大学

报告时间：2024年6月21日（周五）10:00-11:00

报告地点：20-308

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.

报告人简介：曾才斌，教授，博士生导师，华南理工大学统计与金融数学系副主任。主持国自然面上项目2项。近年主要专注于粗糙微分方程的随机吸引子、不变流形与随机混沌的研究，相关结果发表在 J. Funct. Anal.，J. Differential Equations，Proc. Amer. Math. Soc，Chaos 等国际重要数学期刊上。

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