ON TAIL TRIVIALITY OF NEGATIVELY DEPENDENT STOCHASTIC PROCESSES

• 成果类型: Article
• 署名作者: Alishahi, Kasra; Barzegar, Milad; Zamani, Mohammadsadegh
• 署名单位: Sharif University of Technology; University of Yazd
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1626
• 发表日期: 2023
• 页码: 1548-1558
• 关键词: convergence; THEOREM

摘要

We prove that every negatively associated sequence of Bernoulli random variables with summable covariances has a trivial tail a-field. A corollary of this result is the tail triviality of strongly Rayleigh processes. This is a gen-eralization of a result due to Lyons, which establishes tail triviality for dis-crete determinantal processes. We also study the tail behavior of negatively associated Gaussian and Gaussian threshold processes. We show that these processes are tail trivial though, in general, they do not satisfy the summable covariances property. Furthermore, we construct negatively associated Gaus-sian threshold vectors that are not strongly Rayleigh. This identifies a natural family of negatively associated measures that is not a subset of the class of strongly Rayleigh measures.