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

V. Knopova; R. L. Schilling

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arXiv · 1003.1419

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

V. Knopova·R. L. Schilling

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Abstract

We prove several necessary and sufficient conditions for the existence of (smooth) transition probability densities for Lévy processes and isotropic Lévy 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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V. Knopova, R. L. Schilling. 2014-07-29. A note on the existence of transition probability densities for Lévy processes. https://arxiv.org/abs/1003.1419

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