Translator Disclaimer
December, 1980 Compactifications for Dual Processes
Joseph Glover
Ann. Probab. 8(6): 1119-1134 (December, 1980). DOI: 10.1214/aop/1176994573

Abstract

We develop a general theory of duality for Markov processes satisfying Meyer's hypothesis (L) and possessing an excessive reference measure. We make use of a compactification introduced by Walsh which allows a right process and its moderate dual to have strong Markov versions on an enlarged state space. The representation theory for potentials of additive functionals due to Revuz and Sharpe can be extended to this setting. Using this theory, we show that the conatural additive functionals introduced by Garcia-Alvarez are natural additive functionals in the new topology. A general version of Motoo's theorem is given, and the Getoor-Sharpe approach to capacities is extended to this situation. Finally, we show that if the original process satisfies Hunt's hypothesis (H), then a version of the bounded maximum principle holds on the compactified space.

Citation

Download Citation

Joseph Glover. "Compactifications for Dual Processes." Ann. Probab. 8 (6) 1119 - 1134, December, 1980. https://doi.org/10.1214/aop/1176994573

Information

Published: December, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0455.60062
MathSciNet: MR602385
Digital Object Identifier: 10.1214/aop/1176994573

Subjects:
Primary: 60J25
Secondary: 60G99

Rights: Copyright © 1980 Institute of Mathematical Statistics

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.8 • No. 6 • December, 1980
Back to Top