Volume 17, 2013
|Page(s)||567 - 591|
|Published online||01 August 2013|
Moment measures of heavy-tailed renewal point processes: asymptotics and applications
1 Laboratoire LMA, Université de
Poitiers, Téléport 2, BP
2 Department of Mathematics, Uppsala University, Box 480 SE 75106 Uppsala, Sweden
We study higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tailed inter-renewal distribution and its continuous analog, the occupation measure of a heavy-tailed Lévy subordinator. Our results reveal that the asymptotic structure of such moment measures are given by explicit power-law density functions. The same power-law densities appear naturally as cumulant measures of certain Poisson and Gaussian stochastic integrals. This correspondence provides new and extended results regarding the asymptotic fluctuations of heavy-tailed sources under aggregation, and clarifies existing links between renewal models and fractional random processes.
Mathematics Subject Classification: 60K05 / 60G22 / 60F05
Key words: Heavy-tailed renewal process / moment measures / fractional Brownian motion / fractional Poisson motion
© EDP Sciences, SMAI, 2013
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