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Order statistics for jumps of normalised subordinators

Author

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  • Perman, Mihael

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

Suggested Citation

  • Perman, Mihael, 1993. "Order statistics for jumps of normalised subordinators," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 267-281, June.
    • Handle: RePEc:eee:spapps:v:46:y:1993:i:2:p:267-281
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    Cited by:

    1. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.
    2. Yuguang Ipsen & Ross Maller & Soudabeh Shemehsavar, 2020. "Limiting Distributions of Generalised Poisson–Dirichlet Distributions Based on Negative Binomial Processes," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1974-2000, December.
    3. Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    4. Ipsen, Yuguang & Maller, Ross & Shemehsavar, Soudabeh, 2020. "Size biased sampling from the Dickman subordinator," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6880-6900.
    5. Feng, Shui & Gao, Fuqing, 2010. "Asymptotic results for the two-parameter Poisson-Dirichlet distribution," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1159-1177, July.
    6. Nils Lid Hjort & Andrea Ongaro, 2006. "On the distribution of random Dirichlet jumps," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 61-92.
    7. Shi, Quan, 2015. "On the number of large triangles in the Brownian triangulation and fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4321-4350.

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