On the equivalence of three potential principles for right Markov processes
type: Item
instance of: scholarly article
title: On the equivalence of three potential principles for right Markov processes
zbMATH Open document ID: 0668.60065
DOI: 10.1007/BF01197847
publication date: 1990-01-01T00:00:00Z
review text: We examine three of the principles of probabilistic potential theory in a nonclassical setting. These are: (i) the bounded maximum principle, (ii) the positive definiteness of the energy (of measures of bounded potential), and (iii) the condition that each semipolar set is polar. These principles are known to be equivalent in the context of two Markov processes in strong duality, when excessive functions are lower semicontinuous. We show that when the principles are appropriately formulated their equivalence persists in the wider context of a Borel right Markov process X with distinguished excessive measure m. We make no duality hypotheses and m need not be a reference measure. Our main tools are the stationary process \((Y,Q_ m)\) associated with X and m, and a correspondence between potentials \(\mu\) U and certain random measures over \((Y,Q_ m)\).
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 4094528
zbMATH Keywords: principles of probabilistic potential theory
zbMATH Keywords: excessive functions
zbMATH Keywords: right Markov process
zbMATH Keywords: excessive measure
zbMATH Keywords: duality hypotheses
zbMATH Keywords: semipolar
author: Patrick J. Fitzsimmons
reviewed by: Patrick J. Fitzsimmons
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01197847
OpenAlex ID: W1996768106
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4094528