2005/05/10 by Andrew D. Barbour, Alexander Gnedin, Barbour, Andrew D. +2
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.PR #msc:60C05 #msc:60G09
paper · pdf · doi:10.48550/arxiv.math/0505171
arxiv created 2005/05/10 · arxiv updated 2009/12/01
For S a subordinator and Πn an independent Poisson process of intensity ne-x, x>0, we are interested in the number Kn of gaps in the range of S that are hit by at least one point of Πn. Extending previous studies in \citeBernoulli, GPYI, GPYII we focus on the case when the tail of the Lévy measure of S is slowly varying. We view Kn as the terminal value of a random process \cal Kn, and provide an asymptotic analysis of the fluctuations of \cal Kn, as n→∞, for a wide spectrum of situations.