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A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve
Journal article   Peer reviewed

A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve

Alexander Iksanov, Wissem Jedidi and Fethi Bouzeffour
Statistics & probability letters, Vol.126, pp.244-252
07/2017
DOI: https://doi.org/10.1016/j.spl.2017.03.017

Abstract

Bernoulli sieve Infinite occupancy Law of iterated logarithm Perturbed random walk Renewal theory
The Bernoulli sieve is an infinite occupancy scheme obtained by allocating the points of a uniform [0,1] sample over an infinite collection of intervals made up by successive positions of a multiplicative random walk independent of the uniform sample. We prove a law of the iterated logarithm for the number of non-empty (occupied) intervals as the size of the uniform sample becomes large.

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