A note on the existence of transition probability densities for Lévy processes

Mathematics – Probability

Scientific paper

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Scientific paper

We prove several necessary and sufficient conditions for the existence of
(smooth) transition probability densities for L\'evy processes and isotropic
L\'evy processes. Under some mild conditions on the characteristic exponent we
calculate the asymptotic behaviour of the transition density as $t\to 0$ and
$t\to\infty$ and show a ratio-limit theorem.

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