On random fractals with infinite branching: definition, measurability, dimensions

Artemi Berlinkov

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 4, page 1080-1089
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Berlinkov, Artemi. "On random fractals with infinite branching: definition, measurability, dimensions." Annales de l'I.H.P. Probabilités et statistiques 49.4 (2013): 1080-1089. <http://eudml.org/doc/272034>.

@article{Berlinkov2013,
abstract = {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.},
author = {Berlinkov, Artemi},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {packing dimension; Minkowski dimension; random fractal},
language = {eng},
number = {4},
pages = {1080-1089},
publisher = {Gauthier-Villars},
title = {On random fractals with infinite branching: definition, measurability, dimensions},
url = {http://eudml.org/doc/272034},
volume = {49},
year = {2013},
}

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
PB - Gauthier-Villars
VL - 49
IS - 4
SP - 1080
EP - 1089
AB - 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.
LA - eng
KW - packing dimension; Minkowski dimension; random fractal
UR - http://eudml.org/doc/272034
ER -

References

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  12. [12] R. D. Mauldin and M. Urbanski. Conformal iterated function systems with applications to the geometry of continued fractions. Trans. Amer. Math. Soc.351 (1999) 4995–5025. Zbl0940.28009MR1487636
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