Volume 20, 2016
|Page(s)||417 - 431|
|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.
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.