The classical ruin problem on a finite solvable group
For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, “from” a fixed subset, to obtain a new proof of the well-known formula which...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5817 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512039407976448 |
|---|---|
| author | Zhdanova, Yu. D. Жданова, Ю. Д. Жданова, Ю. Д. |
| author_facet | Zhdanova, Yu. D. Жданова, Ю. Д. Жданова, Ю. Д. |
| author_sort | Zhdanova, Yu. D. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:18:35Z |
| description | For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, “from” a fixed subset, to obtain a new proof of the well-known formula which allows one to estimate the characteristic function of the ruin probability (hitting the identity of a group) at the th- trial. |
| first_indexed | 2026-03-24T03:22:27Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5817 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:27Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ed/86bbf6b721e86ccf7bd734b0998e73ed.pdf |
| spelling | umjimathkievua-article-58172020-03-19T09:18:35Z The classical ruin problem on a finite solvable group Классическая задача о разорении на конечной разрешимой группе Zhdanova, Yu. D. Жданова, Ю. Д. Жданова, Ю. Д. For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, “from” a fixed subset, to obtain a new proof of the well-known formula which allows one to estimate the characteristic function of the ruin probability (hitting the identity of a group) at the th- trial. За допомогою явного виразу для характеристичної функції моменту досягнення випадковим блуканням довільної підмножини скінченної розв’язуваної групи “з боку” фіксованої множини для класичної задачі про розорення (окремого випадку циклічної групи) дано нове доведення відомої формули, що дозволяє обчислити характеристичну функцію ймовірності розорення (досягнення одиниці групи) при $t$-му випробуванні. Institute of Mathematics, NAS of Ukraine 1993-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5817 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 3 (1993); 361–366 Український математичний журнал; Том 45 № 3 (1993); 361–366 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5817/8317 https://umj.imath.kiev.ua/index.php/umj/article/view/5817/8318 Copyright (c) 1993 Zhdanova Yu. D. |
| spellingShingle | Zhdanova, Yu. D. Жданова, Ю. Д. Жданова, Ю. Д. The classical ruin problem on a finite solvable group |
| title | The classical ruin problem on a finite solvable group |
| title_alt | Классическая задача о разорении на конечной разрешимой группе |
| title_full | The classical ruin problem on a finite solvable group |
| title_fullStr | The classical ruin problem on a finite solvable group |
| title_full_unstemmed | The classical ruin problem on a finite solvable group |
| title_short | The classical ruin problem on a finite solvable group |
| title_sort | classical ruin problem on a finite solvable group |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5817 |
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