Tohoku Mathematical Journal
2007
March
SECOND SERIES VOL. 59, NO. 1

Tohoku Math. J.
59 (2007), 1-19

Title PARABOLIC HARNACK INEQUALITY FOR THE MIXTURE OF BROWNIAN MOTION AND STABLE PROCESS

Author Renming Song and Zoran Vondraček

(Received July 11, 2005, revised March 22, 2006)
Abstract. 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 $X$.

2000 Mathematics Subject Classification. Primary 60J45; Secondary 60J25, 60J35, 60J75.

Key words and phrases. Parabolic Harnack inequality, parabolic functions, Brownian motion, stable processes, transition density.

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