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Article Dans Une Revue Mathematische Zeitschrift Année : 2008

On Harnack inequality for α-stable Ornstein–Uhlenbeck processes

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Résumé

We consider the α-stable Ornstein–Uhlenbeck process in {\mathbb{R}}^d with the generator TeXL = \Delta^{\alpha/2} - \lambda x \cdot\nabla_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 does not hold.

Dates et versions

hal-03040241 , version 1 (04-12-2020)

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Tomasz Jakubowski. On Harnack inequality for α-stable Ornstein–Uhlenbeck processes. Mathematische Zeitschrift, 2008, 258 (3), pp.609 - 628. ⟨10.1007/s00209-007-0188-2⟩. ⟨hal-03040241⟩
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