For the anisotropic stable JCIR process, the heat kernel exists and obeys a weighted anisotropic Besov bound, the strong Feller property holds, and in the subcritical case convergence to the invariant measure is exponential in total variation.
Heat kernel of anisotropic nonlocal operators
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abstract
We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators.
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2019 1verdicts
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On the anisotropic stable JCIR process
For the anisotropic stable JCIR process, the heat kernel exists and obeys a weighted anisotropic Besov bound, the strong Feller property holds, and in the subcritical case convergence to the invariant measure is exponential in total variation.