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

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

2010-03-06

arxiv.org/abs/1003.1419v2

Mathematics

Probability

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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