| Issue |
ESAIM: PS
Volume 20, 2016
|
|
|---|---|---|
| Page(s) | 417 - 431 | |
| DOI | https://doi.org/10.1051/ps/2016021 | |
| Published online | 30 November 2016 | |
Poisson sphere counting processes with random radii
Division of Mathematical Sciences, School of Physical and Mathematical
Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Nanyang, Singapore.
nprivault@ntu.edu.sg
Received:
10
October
2014
Revised:
13
May
2016
Accepted:
29
July
2016
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.
Mathematics Subject Classification: 60G60 / 60F05
Key words: Random balls / sphere counting / fractional processes / random fields / Poisson stochastic integrals / moment identities
© EDP Sciences, SMAI 2016
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