Mean occupation times of continuous one-dimensional Markov processes

Abstract

We give a general method for finding the long-time asymptotic growth rate of mean occupation times of one-dimensional continuous strong Markov processes. The method uses a well-known decomposition of the resolvent, previous work of Kasahara (1975), and some new comparison results. Particular attention is paid to occupation times measured according to a function which is supported on the whole range of the process. We give an extended example concerning isotropic Brownian flows. A companion paper gives several other examples.