DYNAMIC ASYMPTOTIC RESULTS FOR A GENERALIZED STAR-SHAPED LOSS NETWORK
成果类型：
Article
署名作者：
Graham, Carl; Meleard, Sylvie
署名单位：
Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Sorbonne Universite
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004700
发表日期：
1995
页码：
666-680
关键词：
摘要：
We consider a network in which a call holds a given number of uniformly chosen links and releases them simultaneously. We show pathwise propagation of chaos and convergence of the process of empirical fluctuations to a Gaussian Ornstein-Uhlenbeck process. The limiting martingale problem is obtained by closing a hierarchy. The drift term is given by a simple factorization technique related to mean-field interaction, but the Doob Meyer bracket contains special terms coming from the strong interaction due to simultaneous release. This is treated by closing another hierarchy pertaining to a measure-valued process related to calls routed through couples of links, and the factorization is again related to mean-field interaction. Fine estimates obtained by pathwise interaction graph constructions are used for tightness purposes and are thus shown to be of optimal order.