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Parabolic Harnack Inequality for the Mixture of Brownian Motion and Stable Process

Let $X$ be a mixture of independent Brownian motion and symmetric stable process. In this paper we establish sharp bounds for transition density of $X$, and prove a parabolic Harnack inequality for nonnegative parabolic functions of $X$.

Parabolic Harnack inequality ; parabolic functions ; Brownian motion ; stable processes ; transition density

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