Stochastic Fractals with Markovian Refinements
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 178-192
We consider the random point fields with Markovian refinements we previously introduced. For this class of disordered structures possessing scaling and spatial homogeneity, we give the complete proof of the self-averageability theorem for the fractal dimension.
@article{TMF_2001_128_2_a2,
author = {Yu. P. Virchenko and O. L. Shpilinskaya},
title = {Stochastic {Fractals} with {Markovian} {Refinements}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {178--192},
year = {2001},
volume = {128},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a2/}
}
Yu. P. Virchenko; O. L. Shpilinskaya. Stochastic Fractals with Markovian Refinements. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 178-192. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a2/
[1] Yu. P. Virchenko, O. L. Shpilinskaya, TMF, 124:3 (2000), 490–505 | DOI | MR | Zbl
[2] P. R. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, New York, 1994 | MR | Zbl
[3] G. Federer, Geometricheskaya teoriya mery, Nauka, M., 1987 | MR | Zbl
[4] B. V. Gnedenko, Kurs teorii veroyatnostei, Nauka, M., 1969 | MR
[5] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972 | MR