Nous étudions les questions de la définition et de la mesurabilité des fractales aléatoires avec ramification infinie. Nous trouvons sous certaines conditions une formule pour les dimensions de Minkowski supérieure et inférieure. Pour un d'ensemble aléatoire auto-similaire nous obtenons la dimension.
We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
Mots-clés : packing dimension, Minkowski dimension, random fractal
@article{AIHPB_2013__49_4_1080_0, author = {Berlinkov, Artemi}, title = {On random fractals with infinite branching: definition, measurability, dimensions}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1080--1089}, publisher = {Gauthier-Villars}, volume = {49}, number = {4}, year = {2013}, doi = {10.1214/12-AIHP502}, mrnumber = {3127914}, zbl = {1300.28003}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/12-AIHP502/} }
TY - JOUR AU - Berlinkov, Artemi TI - On random fractals with infinite branching: definition, measurability, dimensions JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 1080 EP - 1089 VL - 49 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/12-AIHP502/ DO - 10.1214/12-AIHP502 LA - en ID - AIHPB_2013__49_4_1080_0 ER -
%0 Journal Article %A Berlinkov, Artemi %T On random fractals with infinite branching: definition, measurability, dimensions %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 1080-1089 %V 49 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/12-AIHP502/ %R 10.1214/12-AIHP502 %G en %F AIHPB_2013__49_4_1080_0
Berlinkov, Artemi. On random fractals with infinite branching: definition, measurability, dimensions. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 4, pp. 1080-1089. doi : 10.1214/12-AIHP502. http://archive.numdam.org/articles/10.1214/12-AIHP502/
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