2014/03/10 by Ottmar Cronie, Cronie, Ottmar, Jorge Mateu +1
Materials Science · Mathematics · #60D05 (Primary) #60G55 (Secondary) #60G57 (Secondary) #60G60 (Secondary) #60J60 #60J70 #60J75 #62M05 #62M09 #62M30 (Secondary) #Collagen: Extraction and Characterization #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1403.2363
openalex publication_date 2014/03/10 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
This paper defines the class of c `adl `ag functional marked point processes\n(CFMPPs). These are (spatio-temporal) point processes marked by random elements\nwhich take values in a c `adl `ag function space, i.e. the marks are given by\nc `adl `ag stochastic processes. We generalise notions of marked\n(spatio-temporal) point processes and indicate how this class, in a sensible\nway, connects the point process framework with the random fields framework. We\nalso show how they can be used to construct a class of spatio-temporal Boolean\nmodels, how to construct different classes of these models by choosing specific\nmark functions, and how c `adl `ag functional marked Cox processes have a\ndouble connection to random fields. We also discuss finite CFMPPs, purely\ntemporally well-defined CFMPPs and Markov CFMPPs. Furthermore, we define\ncharacteristics such as product densities, Palm distributions and conditional\nintensities, in order to develop statistical inference tools such as likelihood\nestimation schemes.\n