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

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  • Iksanov, Alexander
  • Jedidi, Wissem
  • Bouzeffour, Fethi

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.

Suggested Citation

  • Iksanov, Alexander & Jedidi, Wissem & Bouzeffour, Fethi, 2017. "A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 244-252.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:244-252
    DOI: 10.1016/j.spl.2017.03.017
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    References listed on IDEAS

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    1. Alsmeyer, Gerold & Iksanov, Alexander & Marynych, Alexander, 2017. "Functional limit theorems for the number of occupied boxes in the Bernoulli sieve," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 995-1017.
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