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> &...
Saved in:
| Format: | Article |
|---|---|
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/36215 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850176696949407744 |
|---|---|
| collection | DOAJ |
| description | <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> |
| format | Article |
| id | doaj-art-bd44b594554c48fe83b89dedbadef977 |
| institution | OA Journals |
| issn | 1085-3375 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bd44b594554c48fe83b89dedbadef9772025-08-20T02:19:12ZengWileyAbstract and Applied Analysis1085-33752006-01-012006The 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> <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>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/36215 |
| spellingShingle | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types Abstract and Applied Analysis |
| title | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| title_full | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| title_fullStr | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| title_full_unstemmed | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| title_short | The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| title_sort | kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types |
| url | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/36215 |