Regularity conditions in the realisability problem in applications to point processes and random closed sets

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)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Lachièze-Rey, Raphaël and 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:

25 Apr 2017 17:07

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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