Return- and hitting-time limits for rare events of null-recurrent Markov maps

We determine limit distributions for return- and hitting-time functions of certain asymptotically rare events for conservative ergodic infinite measure preserving transformations with regularly varying asymptotic type. Our abstract result applies, in particular, to shrinking cylinders around typical...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2017-02, Vol.37 (1), p.244-276
Main Authors: PÈNE, FRANÇOISE, SAUSSOL, BENOÎT, ZWEIMÜLLER, ROLAND
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Cylinders
Dynamical systems
Ergodic processes
Intervals
Markov analysis
Markov processes
Transformations (mathematics)
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Summary:We determine limit distributions for return- and hitting-time functions of certain asymptotically rare events for conservative ergodic infinite measure preserving transformations with regularly varying asymptotic type. Our abstract result applies, in particular, to shrinking cylinders around typical points of null-recurrent renewal shifts and infinite measure preserving interval maps with neutral fixed points.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2015.38