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Size-biased sampling of Poisson processes and excursions
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Size-biased sampling of Poisson processes and excursions

Author: Mihael Perman; Jim Pitman; Marc Yor
Edition/Format:   Article : English
Publication:Probability theory and related fields, 92, no. 1 (1992), str. 21-39
Database:WorldCat
Summary:
V članku so izpeljane nekatere formule za pristransko vzorčenje iz Poissonovih procesov na abstraktnih prostorih, kjer je velikost točke definirana s poljubno strogo pozitivno funkcijo. Te formule pojasnijo, zakaj lahko v nekaterih primerih (gama in stabilni) predstavimo velikost normaliziranih skokov subordinatorja s shemo residualne alokacije definirane z neodvisnimi slučajnimi spremenljivkami. Rezultati so
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Details

Document Type: Article
All Authors / Contributors: Mihael Perman; Jim Pitman; Marc Yor
ISSN:0178-8051
OCLC Number: 440992810
Description: str. 21-39.
Responsibility: Mihael Perman, Jim Pitman, Marc Yor.

Abstract:

V članku so izpeljane nekatere formule za pristransko vzorčenje iz Poissonovih procesov na abstraktnih prostorih, kjer je velikost točke definirana s poljubno strogo pozitivno funkcijo. Te formule pojasnijo, zakaj lahko v nekaterih primerih (gama in stabilni) predstavimo velikost normaliziranih skokov subordinatorja s shemo residualne alokacije definirane z neodvisnimi slučajnimi spremenljivkami. Rezultati so uporabljeni v primeru pristranega izbiranja ekskurzij Markovega procesa iz rekurentne točke v prostoru stanj s poudarkom na Brownovem gibanju in Besselovih procesih. Predstavljene so tudi povezave z arkus-sinusnim zakonom za delež časa, ko je Brownovo gibanje pozitivno.

Some general formulae are obtained for size_biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to lenght biased sampling of excursions of a Markov process away from a recurrent point in its statespace, with emphasis on the Brownian and Bessel cases when the associated inverse local time is a stable subordinator. Results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by Brownian motion.

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Linked Data


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schema:description"Some general formulae are obtained for size_biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to lenght biased sampling of excursions of a Markov process away from a recurrent point in its statespace, with emphasis on the Brownian and Bessel cases when the associated inverse local time is a stable subordinator. Results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by Brownian motion."
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