The non-uniform Riemann approach to Itô's integral.
type: Item
instance of: scholarly article
title: The non-uniform Riemann approach to Itô's integral.
zbMATH Open document ID: 1067.60025
author: Jing-Yi Tay
author: Tin Lam Toh
author: Tuan Seng Chew
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
review text: This paper proposes two approaches to the Itô's integral in the line of generalized Riemann integrals of the Kurzweil-Henstock-McShane type. It is proved that the two approaches provide a stochastic integral which is equivalent to Itô's one. The definitions are based upon McShane belated divisions, both with variable meshes in the line of the classical Kurzweil-Henstock-McShane integrals. The first definition, motivated by the Henstock lemma for classical integration, makes use of a suitable concept of additive function of meshed intervals. The second definition is a slight modification of a definition of the stochastic integral given by McShane. The basic properties of the integral are proved.
reviewed by: Jean Mawhin
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 2083989
zbMATH Keywords: Kurzweil-Henstock integral
zbMATH Keywords: Itô integral
MaRDI profile type: Publication
full work available at URL: realanalexch.27.2.0495
OpenAlex ID: W1517239135
DOI: 10.14321/REALANALEXCH.27.2.0495
description: scientific article; zbMATH DE number 2083989