COMBINATORIAL LEVY PROCESSES

• 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: 10.1214/17-AAP1306
• 发表日期: 2018
• 页码: 285-339
• 关键词: markov; partitions; networks

摘要

Combinatorial Levy processes evolve on general state spaces of combinatorial structures, of which standard examples include processes on sets, graphs and n-ary relations and more general possibilities are given by processes on graphs with community structure and multilayer networks. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the symmetric difference operation on sets. The main theorems characterize both finite and infinite state space combinatorial Levy processes by a unique s-finite measure. Under the additional assumption of exchangeability, I prove a more explicit characterization by which every exchangeable combinatorial Levy process corresponds to a Poisson point process on the same state space. Associated behavior of the projection into a space of limiting objects reflects certain structural features of the covering process.