A note on capacitary measures of semipolar sets
type: Item
instance of: scholarly article
title: A note on capacitary measures of semipolar sets
zbMATH Open document ID: 0669.60070
author: Mamoru Kanda
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: The author considers a pair of standard processes with stochastic resolvents in strong duality, and he shows that for a Borel set S in the state space satisfying \(S\subset \{P_ S1<\epsilon\), \(\hat P_ S1<\epsilon \}\) for some \(\epsilon\in (0,1]\) (where \(P_ S\), \(\hat P_ S\) denote the respective hitting kernels) there exists a \(\sigma\)-finite measure \(\pi\) on S satisfying the following condition: A Borel subset B of S is polar if and only if \(\pi (B)=0.\) According to a more general result by \textit{C. Dellacherie}, \textit{D. Feyel} and \textit{G.Mokobodzki} [Séminaire de probabilités XVI, Univ. Strasbourg 1980/81, Lect. Notes Math. 920, 8-28 (1982; Zbl 0496.60076)] this property characterizes S to be semipolar. The author shows, moreover, that the measure \(\pi\) may be chosen as the capacitary measure with respect to a \(\lambda\)-subprocess \((\lambda >0)\) provided \(\epsilon <1.\) In a recent preprint ``Remarks on a paper of Kanda'', \textit{P. J. Fitzsimmons} has strengthened the author's result and simplified its proof.
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J40
zbMATH DE Number: 4096526
zbMATH Keywords: semipolar sets
zbMATH Keywords: stochastic resolvents
zbMATH Keywords: strong duality
zbMATH Keywords: capacitary measure
reviewed by: J. Steffens
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991517
OpenAlex ID: W2082124953
DOI: 10.1214/AOP/1176991517
description: scientific article; zbMATH DE number 4096526