Continuity of \(\ell ^ 2\)-valued Ornstein-Uhlenbeck processes
type: Item
instance of: scholarly article
title: Continuity of \(\ell ^ 2\)-valued Ornstein-Uhlenbeck processes
zbMATH Open document ID: 0699.60052
author: Michel Talagrand
author: Joel Zinn
author: Ian Iscoe
author: Michael B. Marcus
author: David R. Mcdonald
published in: The Annals of Probability
publication date: 1990-01-01T00:00:00Z
review text: The authors consider the almost-sure continuity of the following \(\ell^ 2\)-valued Ornstein-Uhlenbeck process given by \[ dX_ t=AX_ tdt+\sqrt{2\alpha}dB_ t, \] where A is a positive, self-adjoint operator on \(\ell^ 2\), \(B_ t\) is a cylindrical Brownian motion on \(\ell^ 2\) and \(\alpha\) is a positive diagonal operator on \(\ell^ 2\). They give a simple sufficient condition for the almost-sure continuity of \(X_ t\) in \(\ell_ 2\) and show that it is quite sharp. Furthermore, they obtain necessary and sufficient conditions in special cases.
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 4147233
zbMATH Keywords: stochastic evolution equations
zbMATH Keywords: almost-sure continuity
zbMATH Keywords: Ornstein- Uhlenbeck process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990938
OpenAlex ID: W2004363445
DOI: 10.1214/AOP/1176990938
description: scientific article; zbMATH DE number 4147233