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.
Additional Metadata
Keywords Boolean model, Càdlàg stochastic process, Conditional intensity, Discrete sampling, Geostatistics with random sampling locations, Intensity functional, LISTA function, Marked reduced Palm measure, Markov process, Maximum (pseudo)likelihood, Pair correlati
THEME Logistics (theme 3), Life Sciences (theme 5)
Publisher Cornell University Library
Series arXiv.org e-Print archive
Citation
Cronie, O.J.A, & Mateu, J. (2014). Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworks. arXiv.org e-Print archive. Cornell University Library .