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

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It...
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Gespeichert in:

Autor*in:	Raphael Lachieze-Rey [verfasserIn] Ilya Molchanov

Format:	Artikel
Sprache:	Englisch

Erschienen:	2015

Rechteinformationen:	Nutzungsrecht: © Copyright 2015 Institute of Mathematical Statistics

Schlagwörter:	Probability Efficiency Correlation analysis Mathematics Mathematical Physics random closed set two-point covering probability 46A40 74A40 47B65 contact distribution function correlation measure 60D05 Point process realisability 28C05 60G55 82D30

Übergeordnetes Werk:	Enthalten in: The annals of applied probability - Cleveland, Ohio : Inst. of Mathematical Statistics, 1991, 25(2015), 1, Seite 116-149
Übergeordnetes Werk:	volume:25 ; year:2015 ; number:1 ; pages:116-149

Links:	Volltext Link aufrufen Link aufrufen Link aufrufen

DOI / URN:	10.1214/13-AAP990

Katalog-ID:	OLC1959666258

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source	Enthalten in The annals of applied probability 25(2015), 1, Seite 116-149 volume:25 year:2015 number:1 pages:116-149
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topic_facet	Probability Efficiency Correlation analysis Mathematics Mathematical Physics random closed set two-point covering probability 46A40 74A40 47B65 contact distribution function correlation measure 60D05 Point process realisability 28C05 60G55 82D30
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author	Raphael Lachieze-Rey
spellingShingle	Raphael Lachieze-Rey ddc 510 misc Probability misc Efficiency misc Correlation analysis misc Mathematics misc Mathematical Physics misc random closed set misc two-point covering probability misc 46A40 misc 74A40 misc 47B65 misc contact distribution function misc correlation measure misc 60D05 misc Point process misc realisability misc 28C05 misc 60G55 misc 82D30 Regularity conditions in the realisability problem with applications to point processes and random closed sets
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topic_title	510 DNB Regularity conditions in the realisability problem with applications to point processes and random closed sets Probability Efficiency Correlation analysis Mathematics Mathematical Physics random closed set two-point covering probability 46A40 74A40 47B65 contact distribution function correlation measure 60D05 Point process realisability 28C05 60G55 82D30
topic	ddc 510 misc Probability misc Efficiency misc Correlation analysis misc Mathematics misc Mathematical Physics misc random closed set misc two-point covering probability misc 46A40 misc 74A40 misc 47B65 misc contact distribution function misc correlation measure misc 60D05 misc Point process misc realisability misc 28C05 misc 60G55 misc 82D30
topic_unstemmed	ddc 510 misc Probability misc Efficiency misc Correlation analysis misc Mathematics misc Mathematical Physics misc random closed set misc two-point covering probability misc 46A40 misc 74A40 misc 47B65 misc contact distribution function misc correlation measure misc 60D05 misc Point process misc realisability misc 28C05 misc 60G55 misc 82D30
topic_browse	ddc 510 misc Probability misc Efficiency misc Correlation analysis misc Mathematics misc Mathematical Physics misc random closed set misc two-point covering probability misc 46A40 misc 74A40 misc 47B65 misc contact distribution function misc correlation measure misc 60D05 misc Point process misc realisability misc 28C05 misc 60G55 misc 82D30
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title	Regularity conditions in the realisability problem with applications to point processes and random closed sets
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title_full	Regularity conditions in the realisability problem with applications to point processes and random closed sets
author_sort	Raphael Lachieze-Rey
journal	The annals of applied probability
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title_sort	regularity conditions in the realisability problem with applications to point processes and random closed sets
title_auth	Regularity conditions in the realisability problem with applications to point processes and random closed sets
abstract	We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension 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 extension 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.
abstractGer	We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension 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 extension 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.
abstract_unstemmed	We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension 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 extension 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.
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title_short	Regularity conditions in the realisability problem with applications to point processes and random closed sets
url	http://dx.doi.org/10.1214/13-AAP990 http://search.proquest.com/docview/1644151656 http://arxiv.org/abs/1102.1950 http://projecteuclid.org/euclid.aoap/1418740181
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up_date	2024-07-03T18:19:49.932Z
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