Symmetric jump processes : localization, heat kernels and convergence
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, p. 59-71

We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.

Nous considérons des processus symétriques purement discontinus. Nous obtenons des estimations locales pour les probabilités de sortie d'une boule, la continuité hölderienne des fonctions harmoniques et des noyaux de la chaleur, et la convergence d'un suite de tels processus.

DOI : https://doi.org/10.1214/08-AIHP201
Classification:  60J35,  60J75,  45K05
Keywords: symmetric jump processes, Dirichlet forms, heat kernels, Harnack inequalities, weak convergence, non-local operators
@article{AIHPB_2010__46_1_59_0,
     author = {Bass, Richard F. and Kassmann, Moritz and Kumagai, Takashi},
     title = {Symmetric jump processes : localization, heat kernels and convergence},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {1},
     year = {2010},
     pages = {59-71},
     doi = {10.1214/08-AIHP201},
     zbl = {1201.60078},
     mrnumber = {2641770},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_1_59_0}
}
Bass, Richard F.; Kassmann, Moritz; Kumagai, Takashi. Symmetric jump processes : localization, heat kernels and convergence. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, pp. 59-71. doi : 10.1214/08-AIHP201. http://www.numdam.org/item/AIHPB_2010__46_1_59_0/

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