The chaotic representation property of compensated-covariation stable families of martingales
type: Item
instance of: scholarly article
title: The chaotic representation property of compensated-covariation stable families of martingales
zbMATH Open document ID: 1360.60091
DOI: 10.1214/15-AOP1066
author: P. Di Tella
author: H.-J. Engelbert
published in: The Annals of Probability
publication date: 2017-01-13T00:00:00Z
review text: The chaotic representation property relates square integrable functionals of some random measure to iterated or multiple integrals. This paper studies a family \(\mathscr X\) of square integrable martingales which is compensated-covariation stable, i.e., such that for any two elements of \(\mathscr X\) the covariation has deterministic compensator and the compensated martingale so obtained is again a member of \(\mathscr X\). The main result of the paper shows that if the set of monomials generated by the given family is total in \(L^2\), then \(\mathscr X\) possesses the chaotic representation property.
reviewed by: Gianluca Cassese
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G46
zbMATH DE Number: 6674843
zbMATH Keywords: square integrable martingales
zbMATH Keywords: chaotic representation property
zbMATH Keywords: Lévy processes
zbMATH Keywords: Teugels martingales
zbMATH Keywords: Hermitian polynomials
zbMATH Keywords: Haar functions
MaRDI profile type: Publication
full work available at URL: 15-aop1066
OpenAlex ID: W2257547994
description: scientific article; zbMATH DE number 6674843