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Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property

Ryad HusseiniMoritz Kassmann — 2009

Annales de l'I.H.P. Probabilités et statistiques

Given a family of Lévy measures ={(, ⋅)}, the present work deals with the regularity of harmonic functions and the Feller property of corresponding jump processes. The main aim is to establish continuity estimates for harmonic functions under weak assumptions on the family . Different from previous contributions the method covers cases where lower bounds on the probability of hitting small sets degenerate.

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