Renewals for exponentially increasing lifetimes, with an application to digital search trees
成果类型：
Article
署名作者：
Dennert, Florian; Gruebel, Rudolf
署名单位：
Leibniz University Hannover
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000862
发表日期：
2007
页码：
676-687
关键词：
摘要：
We show that the number of renewals up to time t exhibits distributional fluctuations as t -> infinity if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of limit laws along subsequences. Our approach can also be used to obtain rates of convergence.