Set indexed strong martingales and path independent variation
type: Item
instance of: scholarly article
title: Set indexed strong martingales and path independent variation
zbMATH Open document ID: 1169.60007
author: Arthur Yosef
published in: Statistics \& Probability Letters
publication date: 2009-04-14T00:00:00Z
review text: Let \((T,\tau)\) be a non-void sigma-compact connected topological space. The author studies strong martingales indexed by an indexed collection \({\mathfrak A}\). By definition, \({\mathfrak A}\) is a family of compact connected subsets of \(T\), satisfying certain conditions. (This notion was introduced by \textit{G. Ivanoff} and \textit{E. Merzbach} [Set-indexed martingales (1999; Zbl 0948.60039)].) It was shown by \textit{R. Cairoli} and \textit{J. B. Walsh} [Acta math. 134, 111--183 (1975; Zbl 0334.60026)] that two-parameter strong martingales satisfying certain conditions show path independent variation (p.i.v.). The author of the present paper extends their results to set-indexed strong martingales (satisfying certain conditions). In the last section the author investigates the p.i.v. property for set-indexed processes having independent increments.
reviewed by: Klaus Schürger
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 5543792
MaRDI profile type: Publication
full work available at URL: j.spl.2008.12.014
OpenAlex ID: W2093142294
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DOI: 10.1016/J.SPL.2008.12.014
description: scientific article; zbMATH DE number 5543792