Bernoulli

The Bernoulli sieve

Alexander V. Gnedin

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Abstract

The Bernoulli sieve is a recursive construction of a random composition (ordered partition) of an integer n. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of components of a stick-breaking interval partition of [0,1]. We exploit the Markov property of the composition and its renewal representation to study the number of its parts. We derive asymptotics of the moments and prove a central limit theorem.

Article information

Source
Bernoulli, Volume 10, Number 1 (2004), 79-96.

Dates
First available in Project Euclid: 23 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1077544604

Digital Object Identifier
doi:10.3150/bj/1077544604

Mathematical Reviews number (MathSciNet)
MR2044594

Zentralblatt MATH identifier
1044.60005

Keywords
composition renewal sampling stick-breaking

Citation

Gnedin, Alexander V. The Bernoulli sieve. Bernoulli 10 (2004), no. 1, 79--96. doi:10.3150/bj/1077544604. https://projecteuclid.org/euclid.bj/1077544604


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