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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 36215, 10 pages
http://dx.doi.org/10.1155/AAA/2006/36215

The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types

1Single Crystal Institute, National Academy of Sciences of Ukraine, Lenin avenue 65, Kharkov 61001, Ukraine
2Belgorod State University, Pobedy 85, Belgorod 308015, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 R. Ye. Brodskii and Yu. P. Virchenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The stochastic model for the description of the so-called fragmentation process in frameworks of Kolmogorov approach is proposed. This model is represented as the branching process with continuum set (0,) of particle types. Each type r(0,) corresponds to the set of fragments having the size r. It is proved that the branching condition of this process represents the basic equation of the Kolmogorov theory.