Tohoku Math. J. (2) 59 (1), 1-19, (2007) DOI: 10.2748/tmj/1176734744
Renming Song, Zoran Vondraček
KEYWORDS: Parabolic Harnock inequality, parabolic functions, Brownian motion, Stable processes, Transition density, 60J45, 60J25, 60J35, 60J75
Let $X$ be a mixture of independent Brownian motion and symmetric stable process. In this paper we establish sharp bounds for transition density of $X$, and prove a parabolic Harnack inequality for nonnegative parabolic functions of $X$.