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May 2018 Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations
Jon Aaronson, Benjamin Weiss
Ann. Inst. H. Poincaré Probab. Statist. 54(2): 879-906 (May 2018). DOI: 10.1214/17-AIHP825

Abstract

In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable – and $\alpha$-rationally ergodic – transformations are presented.

Dans cette note, on identifie les limites distributionnelles des processus stationaires, ergodiques et positives. On montre que toutes se produisent. Les conséquences pour la théorie ergodique infinie sont également explorées et nouveaux exemples de transformations distributionnellement stables – et $\alpha$-rationnellement ergodiques – sont présentées.

Citation

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Jon Aaronson. Benjamin Weiss. "Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations." Ann. Inst. H. Poincaré Probab. Statist. 54 (2) 879 - 906, May 2018. https://doi.org/10.1214/17-AIHP825

Information

Received: 20 July 2016; Revised: 23 January 2017; Accepted: 7 March 2017; Published: May 2018
First available in Project Euclid: 25 April 2018

zbMATH: 06897972
MathSciNet: MR3795070
Digital Object Identifier: 10.1214/17-AIHP825

Subjects:
Primary: 28D, 37A, 60F

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 2 • May 2018
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