Point processes indexed by directed sets
type: Item
instance of: scholarly article
title: Point processes indexed by directed sets
zbMATH Open document ID: 0657.60070
DOI: 10.1016/0304-4149(88)90078-6
author: Gerald Mazziotto
author: Ely Merzbach
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: Point processes are considered in the case where the carrier space is a directed set, not necessarily totally ordered. By extension of the carrier space, it is possible to construct a copy of the point process on a larger carrier space in which the points are now totally-ordered. This permits the construction of a martingale-based theory of point processes. The theory is an alternative to the general one of conditional intensities [see \textit{F. Papangelou}, Z. Wahrscheinlichkeitstheor. verw. Geb. 28, 207-226 (1974; Zbl 0271.60056)] or to the use of marked point processes for spaces like \({\mathbb{R}}^ k\) [see, for example, the reviewer, \textit{B. G. Ivanoff} and \textit{N. C. Weber}, Stochastic Processes Appl. 23, 307-318 (1986; Zbl 0614.60046)].
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 4074108
zbMATH Keywords: dual predictable projection. Point processes
zbMATH Keywords: martingale-based theory of point processes
zbMATH Keywords: conditional intensities
zbMATH Keywords: marked point processes
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90078-6
OpenAlex ID: W1973737399
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description: scientific article; zbMATH DE number 4074108