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Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworks
Stochastics research group, CWIy, Amsterdam, The Netherlands.ORCID iD: 0000-0002-6721-8608
Department of Mathematics, Universitat Jaume I, Campus Riu Sec, Castellón, Spain.ORCID iD: 0000-0002-2868-7604
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper defines the class of càdlàg functional marked point processes (CFMPPs). These are (spatio-temporal) point processes marked by random elements which take values in a càdlàg function space, i.e. the marks are given by càdlàg stochastic processes. We generalise notions of marked (spatio-temporal) point processes and indicate how this class, in a sensible way, connects the point process framework with the random fields framework. We also show how they can be used to construct a class of spatio-temporal Boolean models, how to construct different classes of these models by choosing specific mark functions, and how càdlàg functional marked Cox processes have a double connection to random fields. We also discuss finite CFMPPs, purely temporally well-defined CFMPPs and Markov CFMPPs. Furthermore, we define characteristics such as product densities, Palm distributions and conditional intensities, in order to develop statistical inference tools such as likelihood estimation schemes.

Keywords [en]
Boolean model, Càdlàg stochastic process, Conditional intensity, Discrete sam- pling, Geostatistics with random sampling locations, Intensity functional, LISTA function, Marked reduced Palm measure, Markov process, Maximum (pseudo)likelihood, Pair correlation func- tional, Papangelou conditional intensity, Product density, Random field, Spatio-temporal func- tional marked point process, Spatio-temporal geostatistical marking, Spatio-temporal intensity dependent marks, Wiener measure
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics; Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-145042OAI: oai:DiVA.org:umu-145042DiVA, id: diva2:1183610
Note

arXiv

Available from: 2018-02-18 Created: 2018-02-18 Last updated: 2019-02-22

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Cronie, OttmarMateu, Jorge

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CiteExportLink to record
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  • apa
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