A diffusion process in a Brownian environment with drift
type: Item
instance of: scholarly article
title: A diffusion process in a Brownian environment with drift
zbMATH Open document ID: 0914.60058
author: Kiyoshi Kawazu
author: Hiroshi Tanaka
published in: Journal of the Mathematical Society of Japan
publication date: 1999-06-20T00:00:00Z
review text: Let \(W\) be a Brownian motion and define \(W_\kappa(x):=W(x)-\textstyle {1\over 2}\kappa x\). Furthermore, let \(X^\kappa\) be the process which can be interpreted as the formal solution of the symbolic equation \[ dX(t) =dB(t)-{1\over 2} W_\kappa\bigl(X(t)\bigr)dt, \] where \(B\) is another Brownian motion independent of \(W\). The authors investigate the asymptotic behaviour of that process if \(t\to\infty\) for \(0<\kappa<1\).
reviewed by: Ralf Manthey
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1172190
zbMATH Keywords: diffusion process
zbMATH Keywords: Brownian environment
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04920189
OpenAlex ID: W1988249005
DOI: 10.2969/JMSJ/04920189
description: scientific article; zbMATH DE number 1172190