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

Ryad Husseini; Moritz Kassmann

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1099-1115
  • ISSN: 0246-0203

Abstract

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Given a family of Lévy measures ν={ν(x, ⋅)}x∈ℝd, 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 ν. Different from previous contributions the method covers cases where lower bounds on the probability of hitting small sets degenerate.

How to cite

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Husseini, Ryad, and Kassmann, Moritz. "Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1099-1115. <http://eudml.org/doc/78055>.

@article{Husseini2009,
abstract = {Given a family of Lévy measures ν=\{ν(x, ⋅)\}x∈ℝd, 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 ν. Different from previous contributions the method covers cases where lower bounds on the probability of hitting small sets degenerate.},
author = {Husseini, Ryad, Kassmann, Moritz},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {jump processes; Lévy measure; Feller property; martingale problem; integro-differential operators; harmonic functions; a priori estimates},
language = {eng},
number = {4},
pages = {1099-1115},
publisher = {Gauthier-Villars},
title = {Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property},
url = {http://eudml.org/doc/78055},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Husseini, Ryad
AU - Kassmann, Moritz
TI - Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1099
EP - 1115
AB - Given a family of Lévy measures ν={ν(x, ⋅)}x∈ℝd, 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 ν. Different from previous contributions the method covers cases where lower bounds on the probability of hitting small sets degenerate.
LA - eng
KW - jump processes; Lévy measure; Feller property; martingale problem; integro-differential operators; harmonic functions; a priori estimates
UR - http://eudml.org/doc/78055
ER -

References

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