A new approach to the Martin boundary via diffusions conditioned to hit a compact set
type: Item
instance of: scholarly article
title: A new approach to the Martin boundary via diffusions conditioned to hit a compact set
zbMATH Open document ID: 0777.60075
author: Ross G. Pinsky
published in: The Annals of Probability
publication date: 1993-06-29T00:00:00Z
review text: Let \(L\) be a diffusion generator on an exterior domain. Let \(h\) be the smallest positive solution of \(Lh=0\) with boundary conditions \(h\equiv 1\) on \(\partial D\). Then the harmonic measure boundary at infinity for the \(h\)-transformed diffusion generator \(L^ h\) coincides with the Martin boundary for \(\widetilde {L}\) on \(\mathbb{R}^ d\), the formal adjoint of \(L\). Further the harmonic measure boundary at infinity for the \(\widetilde{h}\)-transformed diffusion generator \(\widetilde{L}^{\widetilde {h}}\) coincides with the Martin boundary for \(L\) on \(\mathbb{R}^ d\). The boundaries are independent of the domain. The impact of these theoretical results is shown by calculation of the boundaries for rotational invariant diffusion generators.
Mathematics Subject Classification ID: 60J50
Mathematics Subject Classification ID: 31C35
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 222716
zbMATH Keywords: diffusion generator on an exterior domain
zbMATH Keywords: harmonic measure boundary at infinity
zbMATH Keywords: Martin boundary
zbMATH Keywords: rotational invariant diffusion generators
reviewed by: Uwe Rösler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989411
OpenAlex ID: W2034802648
DOI: 10.1214/AOP/1176989411
description: scientific article