On the means of approach to the boundary of Brownian motion
type: Item
instance of: scholarly article
title: On the means of approach to the boundary of Brownian motion
zbMATH Open document ID: 0628.60076
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: This paper studies the behavior of a planar Brownian motion as it exists from a simply connected Greenian domain D. The technique is to fix a point \(\xi\) in the Martin boundary of D, and take u to be the Martin kernel with pole at \(\xi\), v its harmonic conjugate, X the u-processes (Brownian motion conditioned to exit D at \(\xi)\), and then to investigate the behavior of the process \((u(X_ t),v(X_ t))\) at the exit time from D. Specializing to the domain \(D=\{z:| z| <1\}\), the results of this paper are used to discuss the connection between the classical and probabilistic Fatou theorems.
reviewed by: Joanna B. Mitro
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4022306
zbMATH Keywords: planar Brownian motion
zbMATH Keywords: Martin boundary
zbMATH Keywords: Martin kernel
zbMATH Keywords: probabilistic Fatou theorems
author: Michael Craig Cranston
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992077
OpenAlex ID: W2003925637
DOI: 10.1214/AOP/1176992077
description: scientific article; zbMATH DE number 4022306