Poisson and Compound Poisson Approximations in a Nonconventional Setup

2012/11/22 by Yuri Kifer, Kifer, Yuri, Ariel Rapaport +1
Mathematics · #37D35 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR #msc:37D35 #msc:60F05

paper · pdf · doi:10.48550/arxiv.1211.5238

slightly revised version

arxiv created 2012/12/10 · arxiv updated 2012/12/11

Abstract

We show that for all ψ-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe completely the asymptotic behavior of these distributions.

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