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.
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}, pages = {59--71}, publisher = {Gauthier-Villars}, volume = {46}, number = {1}, year = {2010}, doi = {10.1214/08-AIHP201}, mrnumber = {2641770}, zbl = {1201.60078}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/08-AIHP201/} }
TY - JOUR AU - Bass, Richard F. AU - Kassmann, Moritz AU - Kumagai, Takashi TI - Symmetric jump processes : localization, heat kernels and convergence JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2010 SP - 59 EP - 71 VL - 46 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/08-AIHP201/ DO - 10.1214/08-AIHP201 LA - en ID - AIHPB_2010__46_1_59_0 ER -
%0 Journal Article %A Bass, Richard F. %A Kassmann, Moritz %A Kumagai, Takashi %T Symmetric jump processes : localization, heat kernels and convergence %J Annales de l'I.H.P. Probabilités et statistiques %D 2010 %P 59-71 %V 46 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/08-AIHP201/ %R 10.1214/08-AIHP201 %G en %F 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://archive.numdam.org/articles/10.1214/08-AIHP201/
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