Vol. 44, No. 1, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
A class of operators on excessive functions

Michael J. Sharpe

Vol. 44 (1973), No. 1, 361–369
Abstract

Let X = (Ω,,t,Xt,𝜃t,Px) be a special standard Markov process with state space (E,g) and transition semigroup (Pt). We emphasize here that the t are the usual completions of the natural σ-fields for the process. In this paper, we associate with certain multiplicative functionals of X operators on the class of excessive functions which are related to the operators PM but which are a bit unusual in probabilistic potential theory in that they are not generally determined by kernels on E ×ℰ. An application is given to a problem treated by P.-A. Meyer concerning natural potentials dominated by an excessive function.

Mathematical Subject Classification 2000
Primary: 60J45
Milestones
Received: 16 September 1971
Published: 1 January 1973
Authors
Michael J. Sharpe