Size-biased sampling of Poisson point processes and excursions

@article{Perman1992SizebiasedSO,
  title={Size-biased sampling of Poisson point processes and excursions},
  author={Mihael Perman and Jim Pitman and Marc Yor},
  journal={Probability Theory and Related Fields},
  year={1992},
  volume={92},
  pages={21-39}
}
SummarySome 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… 
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