Stochastic operator integrals
type: Item
instance of: scholarly article
title: Stochastic operator integrals
zbMATH Open document ID: 0635.60060
DOI: 10.1007/BF01057489
author: N. V. Zhernakov
author: Georgi Us
author: Yurij M. Berezansky
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The authors suggest a construction of an operator stochastic integral of the type \(\int^{\tau}_{0}A(t)dE(t)\), \(\tau\in (0,\infty)\), where \(A(t),\) \(t\in (0,\infty)\), is a family of commuting normal operators in a given separable Hilbert space H and \(E(\Delta),\Delta\in {\mathcal B}(0,\infty)\), is the decomposition of the unit operator in H. Several properties of this integral are established. Let us note that the operator stochastic integral treated here could be considered as a generalization of the well-known stochastic integrals with respect to square integrable martingales.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 4034788
zbMATH Keywords: operator stochastic integral
zbMATH Keywords: square integrable martingales
reviewed by: Jordan Stoyanov
MaRDI profile type: Publication
cites work: Q4118565
cites work: Q5613580
cites work: The Ito-Clifford integral
cites work: Projective spectral theorem
description: scientific article; zbMATH DE number 4034788