A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement
type: Item
instance of: scholarly article
title: A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement
zbMATH Open document ID: 0892.60086
DOI: 10.1023/A:1017946519693
published in: Potential Analysis
publication date: 1998-08-09T00:00:00Z
review text: It is proved that for the standard \(d\)-dimensional Brownian motion \(W\) and any \(\beta<3/2- 1/d\), \(\liminf_{t\to\infty} {1\over t^\beta} \left|\int^t_0 W(s)ds\right|= \infty\) almost surely. As an application, the analogous long time asymptotics for the mean coordinate of a quantum particle with continuously observed position is also obtained when \(d> 2\).
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 81U99
zbMATH DE Number: 1098548
zbMATH Keywords: Brownian motion
zbMATH Keywords: stochastic equation
zbMATH Keywords: quantum filtering
author: Vassili Kolokoltsov
MaRDI profile type: Publication
full work available at URL: a:1017946519693
OpenAlex ID: W209174105
description: scientific article; zbMATH DE number 1098548