主 题: 北京大学数量经济与数理金融教育部重点实验室学术报告——Extremal theory for long range dependent infinitely divisible processes
报告人: Gennady Samorodnitsky (Cornell University)
时 间: 2018-06-11 15:00-16:00
地 点: Room 1560, Sciences Building No. 1
Abstract: We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one regime, our results exhibit limits that are not among the classical extreme value distributions. Restricted to the one-dimensional case, the distributions we obtain interpolate, in the appropriate parameter range, the alpha-Frechet distribution and the skewed alpha-stable distribution. In general, the limit is a new family of stationary and self-similar random sup-measures with parameters alpha in (0,infty) and beta in (0,1), with representations based on intersections of independent beta-stable regenerative sets. The tail of the limit random sup-measure on each interval with finite positive length is regularly varying with index -alpha. The intriguing structure of these random sup-measures is due to intersections of independent beta-stable regenerative sets and the fact that the number of such sets intersecting simultaneously increases to infinity as beta increases to one.
Bio: Gennady Samorodnitsky is a professor of Operations Research and Information Engineering at Cornell University. He is a Fellow of the Institute of Mathematical Statistics, and has served or is serving on many editorial boards, including the Annals of Probability, Annals of Applied Probability, Stochastic Processes and their Applications, Journal of Applied Probability, etc. His research interests include stochastic processes with long memory, heavy tailed stochastic models, extreme value theory, interaction between infinitely divisible processes and ergodic theory and topological data analysis.