Moment measures of heavy-tailed renewal point processes: asymptotics and applications
2013 (English)In: ESAIM. P&S, ISSN 1292-8100, Vol. 17, 567-591 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2013. Vol. 17, 567-591 p.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-214479DOI: 10.1051/ps/2012010ISI: 000330023300015OAI: oai:DiVA.org:uu-214479DiVA: diva2:684893