 Regenerative compositions in the case of slow variationA.D. Barbour and A.V. Gnedin Stochastic Processes and their Applications, 2006, vol. 116, issue 7, 1012-1047 Abstract: For S a subordinator and [Pi]n an independent Poisson process of intensity we are interested in the number Kn of gaps in the range of S that are hit by at least one point of [Pi]n. Extending previous studies in [A.V. Gnedin, The Bernoulli sieve, Bernoulli 10 (2004) 79-96; A.V. Gnedin, J. Pitman, M. Yor, Asymptotic laws for compositions derived from transformed subordinators, Ann. Probab. 2006 (in press). http://arxiv.org/abs/math.PR/0403438, 2004; A.V. Gnedin, J. Pitman, M. Yor, Asymptotic laws for regenerative compositions: gamma subordinators and the like, Probab. Theory Related Fields (2006)] 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 , and provide an asymptotic analysis of the fluctuations of , as n-->[infinity], for a wide spectrum of situations. Keywords: Combinatorial; structure; Component; counts; Slow; variation; Subordinator; Compensator; Regenerative; composition; structure (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:116:y:2006:i:7:p:1012-1047 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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