学术报告报告题目1：Averaging principle and normal deviations for multiscale stochastic systems
报 告 人：解龙杰教授 (江苏师范大学)
报告时间：2021年5月13日（星期四）上午9：00-10:00
报告地点：腾讯会议：会议号593 327 713
报告题目2:Estimating the number of significant components in high-dimensional PCA
报告人：潘光明教授(新加坡南洋理工大学)
报告时间：2021年5月13日（星期四）上午10:00-11:00
报告地点：腾讯会议：会议号593 327 713
邀请人：王绍臣博士
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数学学院
2021年5月12日
报告摘要1：We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central limit type theorems are obtained. In particular, even though the averaged equation for the original system is the same, the corresponding homogenization limit for the normal deviation can be quite different due to the difference in the interactions between the fast scales and the deviation scales. We provide quite intuitive explanations for each case.
报告摘要2：We propose an information criteria to estimate the number of significant components in high-dimensional principal component analysis(PCA).The information criteria is based on the ratio of explained variance and eigenvalue ratios. We show consistency of the estimator in general cases by random matrix theory. We compare its performance with AIC, BIC and some other existing methods for estimating the number of significant components in terms of both theoretical aspects and simulations. An example about the stocks in S&P500 is also reported.