On Harnack inequality for α-stable Ornstein-Uhlenbeck processes
نویسنده
چکیده
We consider the α-stable Ornstein-Uhlenbeck process in Rd with the generator L = ∆α/2 − λx · ∇x. We show that if 2 > α ≥ 1 or α < 1 = d the Harnack inequality holds. For α < 1 < d we construct a counterexample that shows that the Harnack inequality doesn’t hold. keywords: α-stable Ornstein-Uhlenbeck process, harmonic functions, Harnack inequality. AMS Subject Classification: 60J75 60J45
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