On harmonic functions for trace processes
نویسندگان
چکیده
Let X be a standard Markov process with state space E and let F be a closed subset of E. A nonnegative function f on F is extended probabilistically to a function hf on the whole space E. We show that the extension hf is harmonic with respect to X provided that f is harmonic with respect to Y , the trace process on F of the process X . A consequence is that if the Harnack inequality holds for X , it also holds for the trace process Y . Several examples illustrating the usefulness of the result are given.
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