Poisson sphere counting processes with random radii

Privault, Nicolas

ESAIM: Probability and Statistics, Tome 20 (2016), pp. 417-431.

We consider a random sphere covering model made of random balls with interacting random radii of the product form $R(r,\omega )=rG\left(\omega \right)$, based on a Poisson random measure $\omega (dy,dr)$ on $R^d\times R_{+}$. 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.

Classification : 60G60, 60F05
Mots clés : Random balls, sphere counting, fractional processes, random fields, Poisson stochastic integrals, moment identities

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