ORDER-STATISTICS FOR JUMPS OF NORMALIZED SUBORDINATORS

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:46

Article

关键词: POISSON PROCESSES;    SUBORDINATORS;    POISSON-DIRICHLET PROCESS;    INVERSE LOCAL TIME;    DURATION OF EXCURSIONS;   

DOI  :  10.1016/0304-4149(93)90007-Q

来源: Elsevier

【 摘 要 】

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 from 0. For Brownian motion, or more generally, for Bessel processes of dimension delta, 0 < delta < 2, the formulae for the distribution of the n largest atoms are used to find the joint density of the lengths of the n longest excursions away from 0 up to a fixed time. The results are then applied to find expressions for densities of the longest excursion of a Bessel bridge and the density of the longest excursion of a Bessel process completed by a given time.

【 授权许可】

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