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Size-biased sampling of Poisson point processes and excursions

by: M. Perman, J. Pitman, and M. Yor

In: Probability Theory and Related Fields, Vol. 92, Nr. 1Springer (1992) , p. 21--39.

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URL:	http://www.springerlink.com/content/n08754882308h67n/

ome 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 length biased sampling of excursions of a Markov process away from a recurrent point of 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.

BibTeX record

@article{permanpitmanyor92,
  abstract = {ome 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 length biased sampling of excursions of a Markov process away from a recurrent point of 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.},
  added-at = {2010-01-15T19:31:30.000+0100},
  author = {Perman, M. and Pitman, J. and Yor, M.},
  biburl = {http://www.bibsonomy.org/bibtex/2c36b8cb697027e4d7261bae24c95a168/peter.ralph},
  interhash = {995d0b64de56aeabd2e0fa51cf4c508c},
  intrahash = {c36b8cb697027e4d7261bae24c95a168},
  journal = {Probability Theory and Related Fields},
  keywords = {Poisson_process excursions size_biased_parititions},
  number = 1,
  pages = {21--39},
  publisher = {Springer},
  timestamp = {2010-01-15T19:31:30.000+0100},
  title = {{Size-biased sampling of Poisson point processes and excursions}},
  url = {http://www.springerlink.com/content/n08754882308h67n/},
  volume = 92,
  year = 1992
}

Endnote record

%0 Journal Article
%1 permanpitmanyor92
%A Perman, M.
%A Pitman, J.
%A Yor, M.
%D 1992
%I Springer
%J Probability Theory and Related Fields
%K 
%N 1
%P 21--39
%T {Size-biased sampling of Poisson point processes and excursions}
%U http://www.springerlink.com/content/n08754882308h67n/
%V 92
%X ome 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 length biased sampling of excursions of a Markov process away from a recurrent point of 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.

BibSonomy :: publication ::

Size-biased sampling of Poisson point processes and excursions

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Abstract

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Endnote record