Vol. 44, No. 1, 1973

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A class of operators on excessive functions

Michael J. Sharpe

Vol. 44 (1973), No. 1, 361–369

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
Received: 16 September 1971
Published: 1 January 1973
Michael J. Sharpe