The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types
<p>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 <mml:math> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow> &...
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| Format: | Article |
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| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/36215 |
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| Summary: | <p>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 <mml:math> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> of particle types. Each type <mml:math> <mml:mi>r</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> corresponds to the set of fragments having the size <mml:math> <mml:mi>r</mml:mi> </mml:math>. It is proved that the branching condition of this process represents the basic equation of the Kolmogorov theory.</p> |
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| ISSN: | 1085-3375 |