Hitting and returning into rare events for all alpha-mixing processes
By M. Abadi, B. Saussol. 2010
52 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1e629e97260b8d4da1b516a4d026a096dba054d3
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Citations in the corpus
- Entry and return times distribution (2013, background): “his ENTRY AND RETURN TIMES DISTRIBUTION 5 result was proven independently in [52] but follows very easily now from the translation formula. A somewhat generalised version of the theorem was proven in [8]. Lacroix has shown that if F(t) is an eligible limiting distribution, that is it satisfies F(0) =”