Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworks
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||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|
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 .