報(bào)告題目：Asymptotic Behavior of Functional Diffusion Systems with Two-time Scales

報(bào)告人：吳付科教授、博士生導(dǎo)師（華中科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院）

報(bào)告時(shí)間：2017年10月27日（周五）下午16:30

報(bào)告地點(diǎn)：數(shù)學(xué)統(tǒng)計(jì)學(xué)院413會(huì)議室

承辦單位：寧夏大學(xué)數(shù)學(xué)統(tǒng)計(jì)學(xué)院

歡迎廣大師生屆時(shí)光臨！

報(bào)告摘要：This work is concerned with functional diffusions with two-time scales in which the slow-varying component process involve path-dependent functionals and the fast-varying component process is independent of the slow-varying component. When the small parameter tends to zero, asymptotic properties are developed. The martingale method and the weak convergence are adopted to treat this problem. Since the path-dependent functionals are involved, when the martingale method and the weak convergence are used, the functional It\^{o} differential operator will be employed. By treating the fast-varying component process as random "noise", under appropriate conditions, this paper shows that the slow-varying component process involving path-dependent functionals converges weakly to a stochastic process which satisfies a stochastic functional differential equation, in which the coefficients are determined by the invariant measure of the fast-varying component.

報(bào)告人簡(jiǎn)介：教授，博士生導(dǎo)師，2003年博士畢業(yè)于華中科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院。主要從事隨機(jī)微分方程以及相關(guān)領(lǐng)域的研究，2011年入選教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃，2012年入選華中科技大學(xué)“華中學(xué)者”，2014年獲得基金委優(yōu)秀青年基金資助，2015年獲得湖北省自然科學(xué)二等獎(jiǎng)，2017年獲得英國(guó)皇家學(xué)會(huì)"牛頓高級(jí)學(xué)者"基金，SCI期刊《IET Control Theory & Applications》編委。近年來(lái)，在SIAM J. Appl. Math., SIAM J. Numer. Anal., SIAM J. Control Optim., Numer. Math., J. Differential Equations, Automatica和IEEE TAC等國(guó)際權(quán)威期刊發(fā)表論文80余篇，全部為SCI收錄。共主持4項(xiàng)國(guó)家自然科學(xué)基金和一項(xiàng)教育部新世紀(jì)優(yōu)秀人才基金。