SOME MONOTONICITY AND DEPENDENCE PROPERTIES OF SELF-EXCITING POINT PROCESSES
成果类型：
Article
署名作者：
Kwiecinski, Andrzej; Szekli, Ryszard
署名单位：
University of Hamburg; University of Wroclaw
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
1211-1231
关键词：
摘要：
Point processes on the positive real axis which are positively self-exciting in a sense expressed by their martingale dynamics are studied in this paper. It is shown that such processes can be realized as increasing mappings of Poisson processes and are therefore associated in appropriate manners. Some examples are presented, including Hawkes, renewal, Polya-Lundberg, Markov dependent, semi-Markov, in addition to other point processes. As corollaries an extension of theBurton-Waymire association result and a solution of the Glasserman conjecture are obtained. Some results on dependence in stochastic processes of interest in queueing are given as a by product.