On \(L^ p\) stochastic representations
type: Item
instance of: scholarly article
title: On \(L^ p\) stochastic representations
zbMATH Open document ID: 0836.60060
DOI: 10.1016/0167-7152(94)00175-8
author: Yanyan Li
published in: Statistics \& Probability Letters
publication date: 1996-04-22T00:00:00Z
review text: The author proves the following integral representation result for stochastic integrals: Let \(w\) be a Brownian motion on \((\Omega, F^w, P)\). Then \(f \in L_p (F_\infty, P)\), \(1 < p < \infty\), has a representation as \(f = E |f |+ \int^\infty_0 Hdw\), where \(H \in L_p (dw)\), \(L_p (dw) : = \{H \in \wp\mid |H |_\infty < \infty\}\), \(|H |_p = |\int^\infty_0(H^2ds)^{1/2} |_{L_p}\). The representation is unique.
reviewed by: Michael Kohlmann
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 820287
zbMATH Keywords: Brownian motion
zbMATH Keywords: stochastic \(p\)-integral representation
zbMATH Keywords: stochastic integrals
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)00175-8
OpenAlex ID: W1986030693
cites work: Stochastic integration and \(L^ p-\)theory of semimartingales
cites work: Q4139359
cites work: On a stopped Doob's inequality and general stochastic equations
cites work: Q3997782
description: scientific article; zbMATH DE number 820287