Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations

Jon Aaronson; Benjamin Weiss

doi:10.1214/17-AIHP825

Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations

Jon Aaronson, Benjamin Weiss

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 α-rationally ergodic – transformations are presented.

Original language	English
Pages (from-to)	879-906
Number of pages	28
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	54
Issue number	2
DOIs	https://doi.org/10.1214/17-AIHP825
State	Published - May 2018

Bibliographical note

Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2018.

Keywords

Distributional limit
Ergodic stationary process
Infinite ergodic theory
Measure preserving transformation
Normalizing constants
Α-rationally ergodic

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10.1214/17-AIHP825

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Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations

Abstract

Bibliographical note

Keywords

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