Ergodic quasi-exchangeable stationary processes are isomorphic to Bernoulli processes

2019/03/26 by D. Hamdan, Hamdan, Doureid
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Dynamical Systems (math.DS) #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1903.10804

openalex publication_date 2019/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

\abstract\textwidth=4,5 in A discrete time process, with law μ, is quasi-exchangeable if for any finite permutation σ of time indices, the law μ_σ of the resulting process is equivalent to μ. For a quasi-exchangeable stationary process we prove mainly (1) that if the process is ergodic then it is isomorphic to a Bernoulli process and (2) that if the family of all Radon-Nikodym derivatives \dμ_σ\over dμ\ is uniformly integrable then the process is a mixture of Bernoulli processes, which generalizes De Finetti's Theorem. We give application of (1) to some determinantal processes.

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