報(bào)告人：曾才斌教授 華南理工大學(xué)

時(shí)間：2024年5月22日15:00-17:30

地點(diǎn)：數(shù)學(xué)系205室

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 H?lder 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-Schmalfu? 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 Neam?u.

報(bào)告人介紹：曾才斌,，華南理工大學(xué)教授,、博士生導(dǎo)師,、統(tǒng)計(jì)與金融數(shù)學(xué)系副主任,，研究方向?yàn)殡S機(jī)微分動(dòng)力系統(tǒng),，在JFA、JDE等學(xué)術(shù)期刊發(fā)表論文40余篇,，主持承擔(dān)了2項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目,、1項(xiàng)國(guó)家自然科學(xué)基金天元講習(xí)班項(xiàng)目,、國(guó)家自然科學(xué)基金青年項(xiàng)目,、5項(xiàng)省部級(jí)項(xiàng)目，先后學(xué)術(shù)訪問(wèn)猶他州立大學(xué),、赫爾辛基大學(xué),、楊百翰大學(xué)，曾獲廣東省優(yōu)秀博士學(xué)位論文稱號(hào),。