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Regenerative compositions in the case of slow variation


Barbour, A D; Gnedin, A (2006). Regenerative compositions in the case of slow variation. Stochastic Processes and their Applications, 116(7):1012-1047.

Abstract

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 [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 , Kn, as n→∞, for a wide spectrum of situations.

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 [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 , Kn, as n→∞, for a wide spectrum of situations.

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6 citations in Web of Science®
10 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Combinatorial structure; Component counts; Slow variation; Subordinator; Compensator; Regenerative composition structure
Language:English
Date:2006
Deposited On:05 Jan 2010 15:10
Last Modified:05 Apr 2016 13:23
Publisher:Elsevier
ISSN:0304-4149
Publisher DOI:10.1016/j.spa.2005.12.006
Related URLs:http://arxiv.org/abs/math/0505171
Permanent URL: http://doi.org/10.5167/uzh-21591

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