Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction
type: Item
instance of: scholarly article
title: Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction
zbMATH Open document ID: 0953.60034
DOI: 10.1016/S0167-7152(98)00268-5
author: Giacomo Aletti
author: Vincenzo Capasso
published in: Statistics \& Probability Letters
publication date: 2001-02-01T00:00:00Z
review text: The paper investigates the problem of dimension reduction of a plane Poisson process by considering this process along optional increasing paths (OIPs). A convenient characterization of the spatial Poisson process is obtained on the basis of a suitable reparametrization of an OIP that succeeds to transform the process along the path into a one-parameter Poisson process. The key idea within the proof of these results is based on similar facts that hold for one-parameter martingales stopped by a family of bounded stopping times.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 1395192
zbMATH Keywords: martingales
zbMATH Keywords: plane Poisson process
zbMATH Keywords: dimension reduction
zbMATH Keywords: optimal increasing path
zbMATH Keywords: bounded stopping times
MaRDI profile type: Publication
cites work: Stochastic integrals in the plane
cites work: On stopping points in the plane that lie on a unique optional increasing path
cites work: Point processes in the plane
cites work: A characterization of the spatial Poisson process and changing time
cites work: A martingale approach to point processes in the plane
cites work: Q3906202
cites work: Probability with Martingales
full work available at URL: s0167-7152(98)00268-5
OpenAlex ID: W1601099192
description: scientific article; zbMATH DE number 1395192