Poisson sphere counting processes with random radii
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...
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| Format: | Journal Article |
| Language: | English |
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2017
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| Online Access: | https://hdl.handle.net/10356/83340 http://hdl.handle.net/10220/42543 |
| _version_ | 1826118633110110208 |
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| author | Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Privault, Nicolas |
| author_sort | Privault, Nicolas |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T04:47:01Z |
| format | Journal Article |
| id | ntu-10356/83340 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:47:01Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | ntu-10356/833402023-02-28T19:32:39Z Poisson sphere counting processes with random radii Privault, Nicolas School of Physical and Mathematical Sciences Sphere counting Random balls 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. Accepted version 2017-05-31T08:39:48Z 2019-12-06T15:20:19Z 2017-05-31T08:39:48Z 2019-12-06T15:20:19Z 2016 Journal Article Privault, N. (2016). Poisson sphere counting processes with random radii. ESAIM: Probability and Statistics, 20, 417-431. 1292-8100 https://hdl.handle.net/10356/83340 http://hdl.handle.net/10220/42543 10.1051/ps/2016021 en ESAIM: Probability and Statistics © 2016 EDP Sciences, SMAI. This is the author created version of a work that has been peer reviewed and accepted for publication in ESAIM: Probability and Statistics, published by EDP Sciences on behalf of SMAI. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1051/ps/2016021]. 22 p. application/pdf |
| spellingShingle | Sphere counting Random balls Privault, Nicolas Poisson sphere counting processes with random radii |
| title | Poisson sphere counting processes with random radii |
| title_full | Poisson sphere counting processes with random radii |
| title_fullStr | Poisson sphere counting processes with random radii |
| title_full_unstemmed | Poisson sphere counting processes with random radii |
| title_short | Poisson sphere counting processes with random radii |
| title_sort | poisson sphere counting processes with random radii |
| topic | Sphere counting Random balls |
| url | https://hdl.handle.net/10356/83340 http://hdl.handle.net/10220/42543 |
| work_keys_str_mv | AT privaultnicolas poissonspherecountingprocesseswithrandomradii |