Stochastic integration in abstract spaces
type: Item
instance of: scholarly article
title: Stochastic integration in abstract spaces
zbMATH Open document ID: 1202.60077
DOI: 10.1155/2010/217372
author: James K. Brooks
author: J. T. Kozinski
published in: International Journal of Stochastic Analysis
publication date: 2010-09-29T00:00:00Z
full work available at URL: https://eudml.org/doc/224053
review text: Summary: We establish the existence of a stochastic integral in a nuclear space setting as follows. Let \(E\), \(F\), and \(G\) be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions. Assume that there is a continuous bilinear mapping of \(E\times F\) into \(G\). If \(H\) is an integrable, \(E\)-valued predictable process and \(X\) is an \(F\)-valued square integrable martingale, then there exists a \(G\)-valued process \((\int HdX)_t\) called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 5793395
zbMATH Keywords: stochastic integral in a nuclear space
zbMATH Keywords: reflexive, complete, bornological spaces
zbMATH Keywords: convergence theorems
Wikidata QID: Q58651961
MaRDI profile type: Publication
OpenAlex ID: W2147621762
cites work: Q4743520
cites work: Lebesgue-type spaces for vector integration, linear operators, weak completeness and weak compactness
cites work: Q3972791
cites work: Q3957682
cites work: Q5557339
cites work: Q4219712
description: scientific article; zbMATH DE number 5793395