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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.doi:10.2748/tmj/1176734744 fatcat:yupjnymmcfevzpwch7457iiisy