Poisson sphere counting processes with random radii
Date of Issue2016
School of Physical and Mathematical Sciences
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.
ESAIM: Probability and Statistics
© 2016 EDP Sciences, SMAI. This is the author created version of a work that has been peer reviewed and accepted for publication in ESAIM: Probability and Statistics, published by EDP Sciences on behalf of SMAI. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1051/ps/2016021].