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On harmonic functions of symmetric Levy processes (CROSBI ID 184894)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Mimica, Ante On harmonic functions of symmetric Levy processes // Annales de l institut henri poincare-probabilites et statistiques, 50 (2014), 1; 214-235. doi: 10.1214/12-AIHP508

Podaci o odgovornosti

Mimica, Ante

engleski

On harmonic functions of symmetric Levy processes

We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in Bass, Levin '02) 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 Šikić, Song, Vondraček '06 and obtain asymptotic behavior of the Green function and the Lévy density for a large class of subordinate Brownian motions, where the Laplace exponent of the corresponding subordinator is a slowly varying function

geometric stable process; Green function; harmonic function; Levy process; modulus of continuity; subordinator; subordinate Brownian motion

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Podaci o izdanju

50 (1)

2014.

214-235

objavljeno

0246-0203

10.1214/12-AIHP508

Povezanost rada

Matematika

Poveznice
Indeksiranost