On parameter-measurability of the stochastic integral with respect to the two-parameter strong martingale
type: Item
instance of: scholarly article
zbMATH Open document ID: 1245.60053
DOI: 10.1137/S0040585X97985273
publication date: 2012-05-07T00:00:00Z
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 6031479
zbMATH Keywords: two-parameter strong martingale
zbMATH Keywords: quadratic variation
zbMATH Keywords: stochastic integral
MaRDI profile type: Publication
full work available at URL: s0040585x97985273
OpenAlex ID: W2030110724
title: On parameter-measurability of the stochastic integral with respect to the two-parameter strong martingale
published in: Theory of Probability and its Applications
author: N. A. Kolodij
review text: The aim of this article is to establish the existence of a good version of a parametrized family of two-parameters martingales given by stochastic integrals. More precisely, the main result roughly states that, given a measurable family \(\mu(0,x,\omega)\) of \(L^2\)-martingales (where \(0\) sums some measurable space, \(x\in (\mathbb{R}_+)^2\), \(\omega\in\Omega\)) and a measurable family of predictable processes \(f\) that are locally square integrable with respect to \(\mu(0,x,\omega)\), there exists a measurable version of the family of stochastic integrals NEWLINE\[NEWLINE\int_{]0,x]} f(0,x',\omega)\,\mu(0,dx',\omega),NEWLINE\]NEWLINE the quadratic variation of which is given by the integrals of \(f^2\) with respect to the quadratic variation of \(\mu\).
reviewed by: Jacques Franchi
description: scientific article; zbMATH DE number 6031479