Poisson sphere counting processes with random radii
Privault, Nicolas1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Nanyang, Singapore.
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,ω)=rG(ω), based on a Poisson random measure ω(dy,dr) on R d ×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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016021
Classification : 60G60, 60F05
Mots-clés : Random balls, sphere counting, fractional processes, random fields, Poisson stochastic integrals, moment identities
Privault, Nicolas 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Nanyang, Singapore. 
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     zbl = {1355.60065},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2016021/}
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Privault, Nicolas. Poisson sphere counting processes with random radii. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 417-431. doi : 10.1051/ps/2016021. http://www.numdam.org/articles/10.1051/ps/2016021/

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