In this paper we consider the support property and the short time aymptotic behavior of the transition density for (possibly degenerate) processes of jump type whose Lévy measure is singular.
Yashushi Ishikawa. "Support theorem for jump process of canonical type." Proc. Japan Acad. Ser. A Math. Sci. 77 (6) 79 - 83, June 2001. https://doi.org/10.3792/pjaa.77.79