Brodskii, R. Ye.; Virchenko, Yu. P. The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types. (English) Zbl 1131.60085 Abstr. Appl. Anal. 2006, Article ID 36215, 10 p. (2006). Summary: 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 \((0,\infty )\) of particle types. Each type \(r\in (0,\infty )\) 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. MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) PDFBibTeX XMLCite \textit{R. Ye. Brodskii} and \textit{Yu. P. Virchenko}, Abstr. Appl. Anal. 2006, Article ID 36215, 10 p. (2006; Zbl 1131.60085) Full Text: DOI EuDML References: [1] A. F. Filippov, “On the particle size distribution at the subdivision,” Teoriya Veroyatnostei i ee Primenenie, vol. 6, no. 3, pp. 299-318, 1961 (Russian). [2] A. N. Kolmogorov, “On the logarithmically normal distribution law of particle sizes at the subdivision,” Doklady Akademii Nauk SSSR, vol. 31, no. 2, pp. 99-101, 1941 (Russian). [3] B. A. Sevast’yanov, Branching Processes, Nauka, Moscow, 1971. · Zbl 0238.60001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.