hal-00462595, version 1
Hitting and returning into rare events]{Hitting and returning into rare events for all alpha-mixing processes
Abstract: We prove that for any $\alpha$-mixing stationnary process the hitting time of any $n$-string $A_n$ converges, when suitably normalized, to an exponential law. We identify the normalization constant $\lambda(A_n)$. A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem by Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any $n$-string in $n$ consecutive observations, goes to zero as $n$ goes to infinity.
- 1:
- Universidade de São Paulo
- 2:
- CNRS : UMR6205 – Université de Bretagne Occidentale [UBO] – Institut Supérieur des Sciences et Technologies de Brest (ISSTB)
- Domain : Mathematics/Dynamical Systems
- Keywords : alpha mixing – exponential law – return time
- Available versions : v1 (2010-03-25) v2 (2010-05-31)
- hal-00462595, version 1
- http://hal.archives-ouvertes.fr/hal-00462595
- oai:hal.archives-ouvertes.fr:hal-00462595
- From:
- Submitted on: Wednesday, 10 March 2010 12:00:42
- Updated on: Thursday, 25 March 2010 12:05:17
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