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• W2036684501 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 $m$." @default.
• W2036684501 created "2016-06-24" @default.
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• W2036684501 date "2003-01-01" @default.
• W2036684501 modified "2023-10-16" @default.
• W2036684501 title "Homogeneous Random Measures and Strongly Supermedian Kernels of a Markov Process" @default.
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• W2036684501 doi "https://doi.org/10.1214/ejp.v8-142" @default.
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