On diffusions that cannot escape from a convex set
type: Item
instance of: scholarly article
title: On diffusions that cannot escape from a convex set
zbMATH Open document ID: 0684.60059
DOI: 10.1016/0167-7152(89)90127-2
published in: Statistics \& Probability Letters
publication date: 1989-01-01T00:00:00Z
review text: Let X be a diffusion on an open, convex, bounded domain D in \({\mathbb{R}}^ d\). The drift term of X is assumed to be of the form \(\nabla f/f\) where \(f\in C'(D)\), \(f>0\) on D, radial close to \(\partial D\), and vanishes on \(\partial D\). It is seen that Khasminskij's test for nonexplosion takes here the simple form \(\int_{D}(1/f(y))dy=\infty\). This result is applied to derive a large deviation result for Brownian occupation measures.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 4121166
zbMATH Keywords: singular drift
zbMATH Keywords: test for nonexplosion
zbMATH Keywords: large deviation
zbMATH Keywords: Brownian occupation measures
author: A. Korzeniowski
reviewed by: Paavo Salminen
MaRDI profile type: Publication
full work available at URL: 0167-7152(89)90127-2
OpenAlex ID: W2076784245
cites work: Q4099013
cites work: Q5585820
cites work: On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes
cites work: An introduction to the theory of large deviations
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description: scientific article; zbMATH DE number 4121166