On one stochastic model that leads to a stable distribution
We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay...
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5159 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511364560191488 |
|---|---|
| author | Sinaiskii, E. S. Синайский, Е. С. Синайский, Е. С. |
| author_facet | Sinaiskii, E. S. Синайский, Е. С. Синайский, Е. С. |
| author_sort | Sinaiskii, E. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:25:50Z |
| description | We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay time. We invesgigate the approximation of the distribution for sums of values with a given density to the stable distribution law and establish the principal characteristics of the corresponding renewal process. |
| first_indexed | 2026-03-24T03:11:43Z |
| format | Article |
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| id | umjimathkievua-article-5159 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:11:43Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/98/29d47e9d4f9280c61798041be4f1a398.pdf |
| spelling | umjimathkievua-article-51592020-03-18T21:25:50Z On one stochastic model that leads to a stable distribution Об одной стохастической модели, приводящей к устойчивому распределению Sinaiskii, E. S. Синайский, Е. С. Синайский, Е. С. We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay time. We invesgigate the approximation of the distribution for sums of values with a given density to the stable distribution law and establish the principal characteristics of the corresponding renewal process. Інтегральне рівняння, що описує явище післядії, зокрема рівняння стану спадковопружного тіла, інтерпретується як стохастичпа модель з щільністю ймовірності випадкового часу запізнювання у вигляді експоненти дробового порядку Работиова. Вивчається наближення розподілу для сум величин з даною щільністю до стійкого закону розподілу. Встановлюються основні характеристики відповідного процесу відновлення. Institute of Mathematics, NAS of Ukraine 1997-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5159 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 11 (1997); 1572–1579 Український математичний журнал; Том 49 № 11 (1997); 1572–1579 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5159/7014 https://umj.imath.kiev.ua/index.php/umj/article/view/5159/7015 Copyright (c) 1997 Sinaiskii E. S. |
| spellingShingle | Sinaiskii, E. S. Синайский, Е. С. Синайский, Е. С. On one stochastic model that leads to a stable distribution |
| title | On one stochastic model that leads to a stable distribution |
| title_alt | Об одной стохастической модели, приводящей к устойчивому
распределению |
| title_full | On one stochastic model that leads to a stable distribution |
| title_fullStr | On one stochastic model that leads to a stable distribution |
| title_full_unstemmed | On one stochastic model that leads to a stable distribution |
| title_short | On one stochastic model that leads to a stable distribution |
| title_sort | on one stochastic model that leads to a stable distribution |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5159 |
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