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MiS Preprint
53/2008

On hypoellipticity of generators of Lévy processes

Helmut Abels and Ryad Husseini

Abstract

We give a sufficient condition on a Lévy measure $\mu$ which ensures that the generator $L$ of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., the singular support of $u$ is contained in the singular support of $Lu$ for all admissible $u$. In particular, we assume that $\mu$ is smooth away from the origin. We also show that this condition is necessary provided that the support of $\mu$ is compact.

Received:
Aug 14, 2008
Published:
Aug 25, 2008
MSC Codes:
35H10, 35S99, 47G20, 47G30, 60J75
Keywords:
L\'evy processes, L\'evy measures, hypoelliptic, convolution operators, integro-differential operators

Related publications

inJournal
2010 Repository Open Access
Helmut Abels and Ryad Husseini

On hypoellipticity of generators of Lévy processes

In: Arkiv för matematik, 48 (2010) 2, pp. 231-242