Moment measures of heavy-tailed renewal point processes: asymptotics and applications
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 567-591.

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.

DOI : 10.1051/ps/2012010
Classification : 60K05, 60G22, 60F05
Mots clés : Heavy-tailed renewal process, moment measures, fractional brownian motion, fractional Poisson motion
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     title = {Moment measures of heavy-tailed renewal point processes: asymptotics and applications},
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Dombry, Clément; Kaj, Ingemar. Moment measures of heavy-tailed renewal point processes: asymptotics and applications. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 567-591. doi : 10.1051/ps/2012010. http://www.numdam.org/articles/10.1051/ps/2012010/

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