Asymptotic laws for compositions derived from transformed subordinators

• 成果类型: Article
• 署名作者: Gnedin, Alexander; Pitman, Jim; Yor, Marc
• 署名单位: Utrecht University; Sorbonne Universite; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000639
• 发表日期: 2006
• 页码: 468-492
• 关键词: CENTRAL LIMIT-THEOREMS

摘要

A random composition of n appears when the points of a random closed set (R) over tilde subset of [0, 1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts K-n of this composition and other related functionals under the assumption that (R) over tilde = phi(S-center dot), where (S-t, t >= 0) is a subordinator and phi:[0, infinity] -> [0, 1] is a diffeomorphism. We derive the asymptotics of K-n when the Levy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function phi (x) = 1 - e(-x), we establish a connection between the asymptotics of K-n and the exponential functional of the subordinator.