Bernoulli

Partition structures derived from Brownian motion and stable subordinators

Jim Pitman

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Abstract

Explicit formulae are obtained for the distribution of various random partitions of a positive integer n, both ordered and unordered, derived from the zero set M of a Brownian motion by the following scheme: pick n points uniformly at random from [0,1], and classify them by whether they fall in the same or different component intervals of the complement of M. Corresponding results are obtained for M the range of a stable subordinator and for bridges defined by conditioning on 1∈M. These formulae are related to discrete renewal theory by a general method of discretizing a subordinator using the points of an independent homogeneous Poisson process.

Article information

Source
Bernoulli Volume 3, Number 1 (1997), 79-96.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1178291933

Mathematical Reviews number (MathSciNet)
MR1466546

Zentralblatt MATH identifier
0882.60081

Keywords
composition excursion local time random set renewal

Citation

Pitman, Jim. Partition structures derived from Brownian motion and stable subordinators. Bernoulli 3 (1997), no. 1, 79--96.https://projecteuclid.org/euclid.bj/1178291933


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