FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LOCAL STATISTICS OF SPATIAL BIRTH-DEATH PROCESSES IN THE THERMODYNAMIC REGIME

• 成果类型: Article
• 署名作者: Onaran, Efe; Bobrowski, Omer; Adler, Robert J.
• 署名单位: Technion Israel Institute of Technology; University of London; Queen Mary University London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1912
• 发表日期: 2023
• 页码: 3958-3986
• 关键词: continuity; TOPOLOGY

摘要

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.