On hypoellipticity of generators of Lévy processes

Helmut Abels Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, Leipzig, Germany Ryad Husseini Institute for Applied Mathematics, University of Bonn

TBD mathscidoc:1701.333178

Arkiv for Matematik, 48, (2), 231-242, 2008.8
We give a sufficient condition on a Lévy measure$μ$which ensures that the generator$L$of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., $\mathop {\mathrm {sing\,supp}}u\subseteq \mathop {\mathrm {sing\,supp}}Lu$ for all admissible$u$. In particular, we assume that $\mu|_{\mathbb {R}^{d}\setminus \{0\}}\in C^{\infty}(\mathbb {R}^{d}\setminus \{0\})$ . We also show that this condition is necessary provided that $\mathop {\mathrm {supp}}\mu$ is compact.
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  title={On hypoellipticity of generators of Lévy processes},
  author={Helmut Abels, and Ryad Husseini},
  booktitle={Arkiv for Matematik},
Helmut Abels, and Ryad Husseini. On hypoellipticity of generators of Lévy processes. 2008. Vol. 48. In Arkiv for Matematik. pp.231-242. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203628495002987.
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