Stochastic integral equations without probability
type: Item
instance of: scholarly article
title: Stochastic integral equations without probability
zbMATH Open document ID: 0963.60060
DOI: 10.2307/3318668
author: T. Mikosch
author: Rimas Norvaiša
published in: Bernoulli
publication date: 2001-06-13T00:00:00Z
full work available at URL: stochastic-integral-equations-without-probability(1327e0fb-b686-4770-bd37-c707fac44b9b).html
review text: L. C. Young has constructed an extension of the Riemann-Stieltjes integral \(\int_a^b f dh\), where the functions \(f,h:[a,b]\to{\mathbb R}\) have finite \(p\)-variation and finite \(q\)-variation, respectively, with \(p^{-1}+q^{-1}>1\). Motivated by the fact that certain stochastic processes which are not semimartingales may have a bounded \(p\)-variation for some \(p<2\) (like e.g. a large family of Lévy processes, fractional Brownian motions, \dots), the authors investigate some integral equations such as \[ F(y)=F(a)+\int_{a}^{y}F df+g(y)-g(a)\quad \text{and}\quad u(t) =u(0)-\beta\int_{0}^{t}u(s) ds+g(t) -g(0) , \] where the functions \(f,g\) have bounded \(p\)-variation for some \(0<p<2\). Results on the existence and uniqueness of the solution are given.
reviewed by: Jean Bertoin
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 1484638
zbMATH Keywords: \(p\)-variation
zbMATH Keywords: chain rule
zbMATH Keywords: stochastic integral equation
MaRDI profile type: Publication
OpenAlex ID: W2170194190
description: scientific article; zbMATH DE number 1484638