Poisson sphere counting processes with random radii

Author： Privault Nicolas  

Publisher： Edp Sciences

E-ISSN： 1262-3318|20|issue|417-431

ISSN： 1292-8100

Source： ESAIM: Probability and Statistics, Vol.20, Iss.issue, 2016-11, pp. : 417-431

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Abstract

We consider a random sphere covering model made of random balls with interacting random radii of the product form R(r,ω) = rG(ω), based on a Poisson random measure ω(dy,dr) on Rd × R+. We provide sufficient conditions under which the corresponding random ball counting processes are well-defined, and we study the fractional behavior of the associated random fields. The main results rely on moment formulas for Poisson stochastic integrals with random integrands.

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