On a multiple Stratonovich-type integral for some Gaussian processes
type: Item
instance of: scholarly article
title: On a multiple Stratonovich-type integral for some Gaussian processes
zbMATH Open document ID: 1103.60055
author: Maria Jolis
published in: Journal of Theoretical Probability
publication date: 2006-10-31T00:00:00Z
review text: The author constructs a multiple Stratonovich integral with respect to a Gaussian process \(X\) having covariance function of bounded variation on \([0,T]^2\). It is imposed that the integral of a tensor product of functions is the product of the corresponding integrals of order 1. With this definition, it is easy to compute the second order moment of the multiple integral of an elementary function (that is, a finite linear combination of tensor products) by means of Hu-Meyer formula proved for this kind of functions. From this computation, the extension of the integral is obtained by a standard procedure. The integral is then defined on some Banach space of functions.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 5068741
zbMATH Keywords: Itô-type multiple integral
zbMATH Keywords: Stratonovich multiple integral
zbMATH Keywords: Hu-Meyer formula
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s10959-006-0006-5
OpenAlex ID: W2011922518
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DOI: 10.1007/S10959-006-0006-5
description: scientific article