報(bào) 告 人：柳振鑫 教授

報(bào)告題目：The averaging principle for SDEs with monotone coefficients

報(bào)告時(shí)間：2023年8月2日（周三）上午10：00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       柳振鑫，大連理工大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。主要從事隨機(jī)動(dòng)力系統(tǒng)的研究，在隨機(jī)Conley指標(biāo)理論、隨機(jī)動(dòng)力系統(tǒng)中的回復(fù)性和穩(wěn)定性、Kolmogorov平穩(wěn)分布極限問(wèn)題等方面做出系統(tǒng)深入的研究工作。目前已發(fā)表學(xué)術(shù)論文40余篇。2010年獲全國(guó)百篇優(yōu)秀博士學(xué)位論文提名獎(jiǎng)；2015年獲得國(guó)家優(yōu)秀青年科學(xué)基金資助；2019年獲得國(guó)家杰出青年科學(xué)基金資助；2020年入選遼寧省“百千萬(wàn)人才工程”百層次人選；2022年入選大連市優(yōu)秀專(zhuān)家。

報(bào)告摘要：

       Averaging principle is an effective method for investigating multi-scale dynamical systems. In this talk, we will discuss three types of averaging principle for monotone stochastic differential equations, which includes monotone SPDEs, stochastic complex Ginzburg-Landau equations and finite dimensional monotone SDEs. Furthermore, we investigate the small fluctuations of the monotone SDEs around its average, and show that the normalized difference weakly converges to an Ornstein-Uhlenbeck type process, which can be viewed as a functional central limit theorem. This talk is based on joint works with Mengyu Cheng and Michael R?ckner.