Quadratic variation for a class of L lo\(g^ +\,L\)-bounded two-parameter martingales
type: Item
instance of: scholarly article
title: Quadratic variation for a class of L lo\(g^ +\,L\)-bounded two-parameter martingales
zbMATH Open document ID: 0631.60048
author: P. Imkeller
author: Nikos E. Frangos
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: The authors prove that every L log\({}^+ L\)-bounded (not necessarily continuous) two-parameter martingale possesses a quadratic variation in \(L^ 0(\Omega,{\mathcal F},P)\) under the assumption that the one-parameter marginal filtrations \({\mathcal F}^ 1\) and \({\mathcal F}^ 2\) are quasi-left continuous. The technique used is a two-parameter Burkholder-type inequality for martingales indexed by \({\mathbb{N}}^ 2\) and truncation methods that reduce the L log\({}^+ L\)-bounded case to the bounded case. The authors also prove that the bounded martingale that has orthogonal increments or path- independent variation possesses quadratic variation (without hypothesis of quasi-left continuity of \({\mathcal F}^ 1\) and \({\mathcal F}^ 2)\).
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4026464
zbMATH Keywords: two-parameter martingale
zbMATH Keywords: quadratic variation
zbMATH Keywords: two-parameter Burkholder- type inequality
zbMATH Keywords: quasi-left continuity
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992083
OpenAlex ID: W2076644436
DOI: 10.1214/AOP/1176992083
description: scientific article; zbMATH DE number 4026464