The dynamical Borel-Cantelli lemma and the waiting time problems
نویسندگان
چکیده
منابع مشابه
1 3 A pr 2 00 8 THE DYNAMICAL BOREL - CANTELLI LEMMA AND THE WAITING TIME PROBLEMS
We investigate the connection between the dynamical Borel-Cantelli and waiting time results. We prove that if a system has the dynamical BorelCantelli property, then the time needed to enter for the first time in a sequence of small balls scales as the inverse of the measure of the balls. Conversely if we know the waiting time behavior of a system we can prove that certain sequences of decreasi...
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The Borel-Cantelli Lemma is very important in the probability theory. In this paper, we first describe the general case of the Borel-Cantelli Lemma. The first part of this lemma, assuming convergence and the second part includes divergence and independence assumptions. In the following, we have brought generalizations of the first and second part of this lemma. In most generalizat...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2007
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(07)80031-0