Geodesic
Poisson sphere counting processes with random radii
Privault, Nicolas1 idref
1Division 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
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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.

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DOI : 10.1051/ps/2016021
Classification : 60G60, 60F05
Keywords: 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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     author = {Privault, Nicolas},
     title = {Poisson sphere counting processes with random radii },
     journal = {ESAIM: Probability and Statistics},
     pages = {417--431},
     year = {2016},
     publisher = {EDP-Sciences},
     volume = {20},
     doi = {10.1051/ps/2016021},
     zbl = {1355.60065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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

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