Asymptotic laws for regenerative compositions: gamma subordinators and the like
成果类型：
Article
署名作者：
Gnedin, Alexander; Pitman, Jim; Yor, Marc
署名单位：
Utrecht University; University of California System; University of California Berkeley; Sorbonne Universite
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-005-0473-0
发表日期：
2006
页码：
576-602
关键词：
摘要：
For (R) over tilde = 1-exp(-R) a random closed set obtained by exponential transformation of the closed range R of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of (R) over tilde. We focus on the number of parts K-n of the composition when (R) over tilde is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit theorems for K-n and other functionals of the composition such as the number of singletons, doubletons, etc. This study complements our previous work on asymptotics of these functionals when the tail of the Levy measure is regularly varying at 0+.