Abstract
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.
Funding Statement
The second author’s research was financed by DFG (German Science Foundation) through SFB 611.
Citation
Helmut Abels. Ryad Husseini. "On hypoellipticity of generators of Lévy processes." Ark. Mat. 48 (2) 231 - 242, October 2010. https://doi.org/10.1007/s11512-009-0099-z
Information