On random fractals with infinite branching: definition, measurability, dimensions
Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 4, p. 1080-1089

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.

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.

DOI : https://doi.org/10.1214/12-AIHP502
Classification:  28A80,  28A78,  60D05,  37F40
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {4},
     year = {2013},
     pages = {1080-1089},
     doi = {10.1214/12-AIHP502},
     zbl = {1300.28003},
     mrnumber = {3127914},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_4_1080_0}
}
On random fractals with infinite branching: definition, measurability, dimensions. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 4, pp. 1080-1089. doi : 10.1214/12-AIHP502. http://www.numdam.org/item/AIHPB_2013__49_4_1080_0/

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