Abstract and Applied Analysis
Volume 2006 (2006), Article ID 36215, 10 pages
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.
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 of particle types. Each type corresponds to the set of fragments having the
size . It is proved that the branching condition of this
process represents the basic equation of the Kolmogorov theory.