Ergodicity and weak mixing for group-indexed infinitely divisible stationary processes

• 成果类型: Article; Early Access
• 署名作者: Avraham-Re'em, Nachi; Roy, Emmanuel
• 署名单位: Technion Israel Institute of Technology; Universite Paris 13
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01522-9
• 发表日期: 2026-07-20
• 关键词: Stationary process; Infinitely divisible process; ergodicity; Weak mixing; REPRESENTATIONS; EQUIVALENCE; NULL

摘要

We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity implies weak mixing is intrinsic to infinite divisibility, removing all structural assumptions on the group from prior results. The main ingredient is a general construction of stochastically continuous extensions for separable in probability stationary processes, reducing the problem to stochastically continuous processes indexed by Polish groups and then to countable groups, where we combine the Maruyama representation with an ergodicity criterion for Poisson suspensions.