Fuk's inequalities for stochastic fields of reversed martingales
type: Item
instance of: scholarly article
title: Fuk's inequalities for stochastic fields of reversed martingales
zbMATH Open document ID: 0743.60048
DOI: 10.1007/BF00972782
published in: Siberian Mathematical Journal
publication date: 1992-06-26T00:00:00Z
review text: Let \(\{X_ n, n\in\mathbb{Z}^ d\}\) be a family of random variables adapted to a backward filtration \(\{{\mathcal F}_ n, n\in \mathbb{Z}^ d\}\) whereas the usual partial ordering in \(\mathbb{Z}^ d\) is adopted. Let, for any \(m,n\in\mathbb{Z}^ d\) with \(m<n\), \(E(X_ m\mid {\mathcal F}_ n)=0\) a.s. hold. Several inequalities for the backward martingale \(S_ n=\sum_{k\geq n}X_ k\) are proved.
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 20692
zbMATH Keywords: martingales with multidimensional parameters
zbMATH Keywords: martingale inequalities
zbMATH Keywords: backward filtration
zbMATH Keywords: backward martingale
author: Zbigniew A. Lagodowski
reviewed by: M.P.Jerschow
MaRDI profile type: Publication
cites work: Stochastic integrals in the plane
cites work: Sums of independent random variables on partially ordered sets
full work available at URL: https://doi.org/10.1007/bf00972782
OpenAlex ID: W2087567608
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description: scientific article; zbMATH DE number 20692