讲座题目：Extreme value theory for a sequence of suprema of a class of Gaussian processes with trend
讲座时间：2024年5月8日下午16:00-1700
讲座地点：线上腾讯会议929-786-426; 会议密码0508
主讲人简介：Dr. Ji is a lecturer (tenured) in the Department of Statistics at the University of Leeds. He obtained his Ph.D. degree in Actuarial Science at University of Lausanne (UNIL) and was awarded "Prix de la Fondation Nicolas et Helene Porphyrogenis 2014" for his excellent Ph.D. thesis. After his Ph.D. he worked as a Postdoc researcher at UNIL from Feb 2014 to April 2016 and at University of Applied Science of Western Switzerland from May 2016 to Dec 2017. So far, he has made contributions to various research areas, including actuarial mathematics, risk theory, Bayesian CART, extreme value theory and Gaussian random fields. He has published about 40 papers in academic journals on probability theory, applied probability statistics and actuarial science, including top-tier journals like Annals of Probability, Stochastic Processes and Their Applications, Transactions of the American Mathematical Society, Scandinavia Actuarial Journal and Insurance: Mathematics and Economics. He also serves as an editorial board member for the academic journal Risks.
讲座内容简介：In this talk, we shall discuss the extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its theoretical interestingness. We consider both stationary sequences and non-stationary sequences obtained by considering whether the trend functions are identical or not. We show that a sequence of suitably normalised kth order statistics converges in distribution to a limiting random variable which can be a negative log transformed Erlang distributed random variable, a Normal random variable or a mixture of them, according to three conditions deduced through the model parameters. Remarkably, this phenomenon resembles that for the stationary Normal sequence. We also show that various moments of the normalised kth order statistics converge to the moments of the corresponding limiting random variable. The obtained results enable us to investigatevarious properties of these random sequences, which reveals interesting particularities of this class of random sequences in extreme value theory.
主办：数学学院
