174 research outputs found
Scaling invariant Harnack inequalities in a general setting
In a setting, where only "exit measures" are given, as they are associated
with an arbitrary right continuous strong Markov process on a separable metric
space, we provide simple criteria for the validity of Harnack inequalities for
positive harmonic functions. These inequalities are scaling invariant with
respect to a metric on the state space which, having an associated Green
function, may be adapted to the special situation. In many cases, this also
implies continuity of harmonic functions and H\"older continuity of bounded
harmonic functions. The results apply to large classes of L\'evy (and similar)
processes
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