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The general asymptotic return-time process

Authors
  • Zweimüller, Roland1
  • 1 Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, Wien, 1090, Auatria , Wien (Austria)
Type
Published Article
Journal
Israel Journal of Mathematics
Publisher
The Hebrew University Magnes Press
Publication Date
May 24, 2016
Volume
212
Issue
1
Pages
1–36
Identifiers
DOI: 10.1007/s11856-016-1293-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

We study limit processes for consecutive return-times of asymptotically rare events in general ergodic probability preserving systems. It is shown that in every ergodic system on a non-atomic space any non-negative stationary sequence with expectation not exceeding 1 occurs as a limit process. Moreover, the limiting behaviour is shown to be robust under small changes of the sets. We also determine the relation between asymptotic return-time processes and asymptotic hitting-time processes, and record some consequences.

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