On harmonic functions of symmetric Lévy processes

Ante Mimica

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 1, page 214-235
  • ISSN: 0246-0203

Abstract

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We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (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 (Probab. Theory Related Fields135 (2006) 547–575) 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.

How to cite

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Mimica, Ante. "On harmonic functions of symmetric Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 50.1 (2014): 214-235. <http://eudml.org/doc/272055>.

@article{Mimica2014,
abstract = {We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (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 (Probab. Theory Related Fields135 (2006) 547–575) 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.},
author = {Mimica, Ante},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {geometric stable process; Green function; harmonic function; Lévy process; modulus of continuity; subordinator; subordinate brownian motion; subordinate Brownian motion},
language = {eng},
number = {1},
pages = {214-235},
publisher = {Gauthier-Villars},
title = {On harmonic functions of symmetric Lévy processes},
url = {http://eudml.org/doc/272055},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Mimica, Ante
TI - On harmonic functions of symmetric Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 1
SP - 214
EP - 235
AB - We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (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 (Probab. Theory Related Fields135 (2006) 547–575) 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.
LA - eng
KW - geometric stable process; Green function; harmonic function; Lévy process; modulus of continuity; subordinator; subordinate brownian motion; subordinate Brownian motion
UR - http://eudml.org/doc/272055
ER -

References

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