Order statistics for jumps of normalised subordinators

Mihael Perman

Stochastic Processes and their Applications, 1993, vol. 46, issue 2, 267-281

Abstract: A subordinator is a process with independent, stationary, non-negative increments. On the unit interval we can view this process as the distribution function of a random measure, and, dividing this random measure by its total mass, we get a random discrete probability distribution. Formulae for the joint distribution of the n largest atoms in this distribution are derived. They are used to derive some results about the Poisson-Dirichlet process. Subordinators arise as inverse local times of diffusions and the atoms in the random measure associated with them correspond to the lengths of excursions of the diffusion away form 0. For Brownian motion, or more generally, for Bessel processes of dimension [delta], 0

Keywords: Poisson; processes; subordinators; Poisson-Dirichlet; process; inverse; local; time; duration; of; excursions (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (7)

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