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

Husseini, Ryad; Kassmann, Moritz

Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, p. 1099-1115 / Harvested from Project Euclid

Résumé

Given a family of Lévy measures ν={ν(x, ⋅)}_x∈ℝ^d, 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.

Publié le : 2009-11-15
Classification: Jump processes, Lévy measure, Feller property, Martingale problem, Integro-differential operators, Harmonic functions, A priori estimates, 60J75, 35B45, 31C05, 47D07

@article{1257529894,
     author = {Husseini, Ryad and Kassmann, Moritz},
     title = {Jump processes, L-harmonic functions, continuity estimates and the Feller property},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {45},
     number = {1},
     year = {2009},
     pages = { 1099-1115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257529894}
}

Husseini, Ryad; Kassmann, Moritz. Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp.  1099-1115. http://gdmltest.u-ga.fr/item/1257529894/