On harmonic functions of symmetric Levy processes (CROSBI ID 184894)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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