SIZE-BIASED SAMPLING OF POISSON POINT-PROCESSES AND EXCURSIONS

• 成果类型: Article
• 署名作者: PERMAN, M; PITMAN, J; YOR, M
• 署名单位: Sorbonne Universite; University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01205234
• 发表日期: 1992
• 页码: 21-39
• 关键词: neutral alleles; distributions; continuity; MODEL

摘要

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 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.