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Article Dans Une Revue Monatshefte für Mathematik Année : 2023

Ergodic quasi-exchangeable stationary processes are isomorphic to Bernoulli processes

Résumé

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, our main results are (1) if the process is ergodic then it is isomorphic to a Bernoulli process and (2) if the family of all Radon-Nikodym derivatives {dµ^σ/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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Dates et versions

hal-03904057 , version 1 (16-12-2022)

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Doureid Hamdan. Ergodic quasi-exchangeable stationary processes are isomorphic to Bernoulli processes. Monatshefte für Mathematik, 2023, 200 (1), pp.93-117. ⟨10.1007/s00605-022-01779-x⟩. ⟨hal-03904057⟩
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