DYNAMIC RANDOM NETWORKS AND THEIR GRAPH LIMITS
成果类型：
Article
署名作者：
Crane, Harry
署名单位：
Rutgers University System; Rutgers University New Brunswick
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/15-AAP1098
发表日期：
2016
页码：
691-721
关键词：
摘要：
We study a broad class of stochastic process models for dynamic networks that satisfy the minimal regularity conditions of (i) exchangeability and (ii) cadlag sample paths. Our main theorems characterize these processes through their induced behavior in the space of graph limits. Under the assumption of time-homogeneous Markovian dependence, we classify the dis-continuities of these processes into three types, prove bounded variation of the sample paths in graph limit space and express the process as a mixture of time-inhomogeneous, exchangeable Markov processes with cadlag sample paths.