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Hitting-time limits for some exceptional rare events of ergodic maps

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  • Zweimüller, Roland

Abstract

We discuss limit distributions for hitting-time functions of certain “exceptional” families of asymptotically rare events for ergodic probability preserving transformations. The abstract core is an inducing argument. The latter applies, for example, to shrinking intervals around periodic points (both uniformly expanding and neutral) of certain finite measure preserving interval maps. In particular, we give a complete answer to a question raised in Freitas et al. (2016).

Suggested Citation

  • Zweimüller, Roland, 2019. "Hitting-time limits for some exceptional rare events of ergodic maps," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1556-1567.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:5:p:1556-1567
    DOI: 10.1016/j.spa.2018.05.011
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    1. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike & Vaienti, Sandro, 2016. "Rare events for the Manneville–Pomeau map," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3463-3479.
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