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

Alexander Iksanov; Wissem Jedidi; Fethi Bouzeffour

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arXiv · 1609.09238

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

Alexander Iksanov·Wissem Jedidi·Fethi Bouzeffour

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Abstract

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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Alexander Iksanov, Wissem Jedidi, Fethi Bouzeffour. 2016-09-29. A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve. https://arxiv.org/abs/1609.09238

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