Poisson sphere counting processes with random radii

Privault, Nicolas

doi:10.1051/ps/2016021

Geodesic

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Poisson sphere counting processes with random radii

Privault, Nicolas ¹

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

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Résumé

We consider a random sphere covering model made of random balls with interacting random radii of the product form $R (r, ω) = r G (ω)$ , based on a Poisson random measure $ω (d y, d r)$ 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.

Reçu le : 2014-10-10
Accepté le : 2016-07-29

Zbl

DOI : 10.1051/ps/2016021

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

Affiliations des auteurs :

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},
     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     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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