Lidan Wang, University of Washington
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THO 235
A generic strong Markov process may have both the continuous (diffusive) part and the purely discontinuous (jumping) part, and its infinitesimal generator is a mixture of local and non-local operators.
Suppose a strong Markov process $X$ has a jointly continuous transition density function with two-sided estimates that contain both the Gaussian and the power law components, we will show that under certain Kato class conditions, the heat kernel of a non-local Feynman-Kac semigroup of $X$ has similar two-sided estimates, but with a set of possible different constants.