@article{EJP142,
author = {Patrick Fitzsimmons and Ronald Getoor},
title = {Homogeneous Random Measures and Strongly Supermedian Kernels of a Markov Process},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {8},
year = {2003},
keywords = {Homogeneous random measure, additive functional, Kuznetsov measure, potential kernel, characteristic measure, strongly supermedian, smooth measure.},
abstract = {The potential kernel of a positive left additive functional (of a strong Markov process $X$) maps positive functions to strongly supermedian functions and satisfies a variant of the classical domination principle of potential theory. Such a kernel $V$ is called a regular strongly supermedian kernel in recent work of L. Beznea and N. Boboc. We establish the converse: Every regular strongly supermedian kernel $V$ is the potential kernel of a random measure homogeneous on $[0,\infty[$. Under additional finiteness conditions such random measures give rise to left additive functionals. We investigate such random measures, their potential kernels, and their associated characteristic measures. Given a left additive functional $A$ (not necessarily continuous), we give an explicit construction of a simple Markov process $Z$ whose resolvent has initial kernel equal to the potential kernel $U_{\!A}$. The theory we develop is the probabilistic counterpart of the work of Beznea and Boboc. Our main tool is the Kuznetsov process associated with $X$ and a given excessive measure $m$.},
pages = {no. 10, 1-54},
issn = {1083-6489},
doi = {10.1214/EJP.v8-142},
url = {http://ejp.ejpecp.org/article/view/142}}