Speaker:  Prof. Xiangfeng Yang (杨香凤）, Linköping University,  Sweden

Title: Longest gaps between epochs in Poisson processes

Time：2018-01-04， 14:00-15:00

Venue：Room 316 of Environment Building, Renmin University

Abstract:

The longest gap L(t) up to time t in a Poisson process (N(t)) is the maximal time subinterval between epochs of arrival times up to time t; and it finds applications in the theory of reliability. If the Poisson process is homogeneous, then the laws of large numbers of L(t) have been known since the 1980s, and in this talk I will present new results on exact asymptotics for the large deviation probabilities. If the Poisson process is inhomogeneous, then laws of large numbers of L(t) have not yet been explicitly established in the literature, and in this talk I will present such laws. The main tool is to establish global and local estimations of the distribution function of L(t) based on discretization arguments and the Slivnyak`s formula of Palm theory.