On integration with respect to the \(q\)-Brownian motion
type: Item
instance of: scholarly article
title: On integration with respect to the \(q\)-Brownian motion
zbMATH Open document ID: 1321.60114
published in: Statistics \& Probability Letters
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1407.7090
review text: Based on the author's abstract: The author uses the Jackson \(q\)-integral to define integration with respect to the so called \(q\)-Brownian motion, for a parameter \(0 < q < 1\). The main results of the paper are the \(q\)-analogues of the \(L^2\)-isometry and of the Itō formula for polynomial integrands. It is also indicated how the \(L^2\)-isometry extends the integral to more general functions.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 6363291
zbMATH Keywords: \(q\)-Brownian motion
zbMATH Keywords: stochastic integration
zbMATH Keywords: Itō formula
zbMATH Keywords: stochastic quantum calculus
author: Włodek Bryc
reviewed by: Pavel Gapeev
MaRDI profile type: Publication
OpenAlex ID: W1981993561
arXiv ID: 1407.7090
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DOI: 10.1016/J.SPL.2014.07.029
description: scientific article; zbMATH DE number 6363291