学术报告报 告人：Xue-Mei Li教授（英国帝国理工大学）
报告时间：2022年12月9日（星期五）下午4:30-- 5:30
报告地点：腾讯会议：484-419-896，密码：221209
邀 请人：曾才斌 副教授
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数学学院
2022年11月28日
报告摘要：Multi-scale dynamics is prevalent and so is stochastic multi-scale systems. The aim is to the persistent effect of the fast motion on the slow motion and obtain the effective motion for the slow variable as the time scale separation parameter is taken to zero. This fundamental concept is at the heart of balancing the need of delicate more precise modelling and the need to extract information from the model. Yet studies until recently had been restricted on deterministic systems or systems with noise which are locally uncorrelated. Recently we embarked on the study of multi-scale stochastic differential equations driven by an autocorrelated stationary increment Gaussian process (fractional Brownian motions) with non-trivial multiplicative noise. Classical methods do not seem to apply, there are some very interesting and exciting new results.
报告人简介：Xue-Mei Li is a professor of Imperial College London and a professor of EPFL (Chair of Stochastic Analysis). She studied in England from 1988-1992. In her PhD thesis she solved the open problem on the existence of smooth stochastic flows on non-compact manifold, and introduced a differentiation formula for the derivative of the probability semi-groups which does not depend on the derivative of the initial value of the parabolic equation which later was shown to be equivalent to the integration by parts formula on path spaces. The novel proof has led to a surge of activity and the application to the unique ergodicity problem for stochastic partial differential equations (SPDEs). Since then she worked on the geometry of diffusion operators, analysis of measures and Sobolev calculus on path spaces, and stability problems. She is also one of the first people who studied the properties of strict local martingales (a terminology introduced in an article coauthored by her). Her recent work is on slow/fast systems on manifolds, reduction of perturbed stochastic systems with conservation laws, and more recently on fluctuation theory of SPDEs, slow fast SPDEs with fractional Brownian motion among other interests. She has pioneered with Fractional Averaging and co-authored the first article on homogenisation with fractional noise, also obtained the first rough Functional Limit Theorem (CLT).