Lachièze-Rey, Raphaël; Molchanov, Ilya (2015). Regularity conditions in the realisability problem in applications to point processes and random closed sets. Annals of applied probability, 25(1), pp. 116-149. Institute of Mathematical Statistics 10.1214/13-AAP990
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We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Lachièze-Rey, Raphaël, Molchanov, Ilya |
Subjects: |
300 Social sciences, sociology & anthropology > 360 Social problems & social services 500 Science > 510 Mathematics |
ISSN: |
1050-5164 |
Publisher: |
Institute of Mathematical Statistics |
Language: |
English |
Submitter: |
Lutz Dümbgen |
Date Deposited: |
28 Oct 2015 11:47 |
Last Modified: |
05 Dec 2022 14:49 |
Publisher DOI: |
10.1214/13-AAP990 |
ArXiv ID: |
0907.0077 |
BORIS DOI: |
10.7892/boris.72279 |
URI: |
https://boris.unibe.ch/id/eprint/72279 |
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