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We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (
(2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from (
(2006) 547–575) and obtain asymptotic behavior of the...
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