A sharp and strict \(L^ p\)-inequality for stochastic integrals
type: Item
instance of: scholarly article
title: A sharp and strict \(L^ p\)-inequality for stochastic integrals
zbMATH Open document ID: 0617.60042
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: Let M be a right-continuous martingale, V be a predictable process, \(N=V\circ M\) (stochastic integral of V with respect to M). Let \(p^*\) be the maximum of p and q where \(1<p<\infty\) and \(1/p+1/q=1\). Set \(\| M\|_ p=\sup_{t}\| M_ t\|_ p.\) Theorem. If \(p=2\) and \(0<\| M\|_ p<\infty\), then \[ \| N\|_ p<(p^*-1)\| M\|_ p \] [strict inequality in contrast with a previous result of the author, see ibid. 12, 647-702 (1984; Zbl 0556.60021)].
reviewed by: Yuri Kabanov
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4001109
zbMATH Keywords: norm inequalities
zbMATH Keywords: right-continuous martingale
zbMATH Keywords: predictable process
author: Donald L. Burkholder
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992268
OpenAlex ID: W2051401885
DOI: 10.1214/AOP/1176992268
description: scientific article; zbMATH DE number 4001109