Measure-valued diffusion
We consider the class of continuous measure-valued processes {μ t } on a finite-dimensional Euclidean space X for which ∫fd μ t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R smooth enough. It is shown that, under some general condition, the Markov...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5018 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511212010209280 |
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| author | Skorokhod, A. V. Скороход, А. В. |
| author_facet | Skorokhod, A. V. Скороход, А. В. |
| author_sort | Skorokhod, A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:53Z |
| description | We consider the class of continuous measure-valued processes {μ t } on a finite-dimensional Euclidean space X for which ∫fd μ t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R smooth enough. It is shown that, under some general condition, the Markov process with this property can be obtained as a weak limit for systems of randomly interacting particles that are moving in X along the trajectories of a diffusion process in X as the number of particles increases to infinity. |
| first_indexed | 2026-03-24T03:09:18Z |
| format | Article |
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| id | umjimathkievua-article-5018 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:09:18Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b8/98b69526d79004312f3f6657dacd7bb8.pdf |
| spelling | umjimathkievua-article-50182020-03-18T21:22:53Z Measure-valued diffusion Мірозначна дифузія Skorokhod, A. V. Скороход, А. В. We consider the class of continuous measure-valued processes {μ t } on a finite-dimensional Euclidean space X for which ∫fd μ t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R smooth enough. It is shown that, under some general condition, the Markov process with this property can be obtained as a weak limit for systems of randomly interacting particles that are moving in X along the trajectories of a diffusion process in X as the number of particles increases to infinity. Розглядається клас неперервних мірозначних процесів {μ t } на скінченновимірному евклідовому просторі X, для якого ∫fd μ t — семімартингал з характеристикою, що є абсолютно неперервною відносно t для всіх досить гладких t for all f:X→R. Показано, що при досить загальних умовах марковський процес з цією властивістю може бути отриманий як слабка границя для систем випадково взаємодіючих частинок, що рухаються в X уздовж траєкторій дифузійного процесу в X, коли число частинок зростає до нескінченності. Institute of Mathematics, NAS of Ukraine 1997-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5018 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 3 (1997); 458–464 Український математичний журнал; Том 49 № 3 (1997); 458–464 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5018/6735 https://umj.imath.kiev.ua/index.php/umj/article/view/5018/6736 Copyright (c) 1997 Skorokhod A. V. |
| spellingShingle | Skorokhod, A. V. Скороход, А. В. Measure-valued diffusion |
| title | Measure-valued diffusion |
| title_alt | Мірозначна дифузія |
| title_full | Measure-valued diffusion |
| title_fullStr | Measure-valued diffusion |
| title_full_unstemmed | Measure-valued diffusion |
| title_short | Measure-valued diffusion |
| title_sort | measure-valued diffusion |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5018 |
| work_keys_str_mv | AT skorokhodav measurevalueddiffusion AT skorohodav measurevalueddiffusion AT skorokhodav míroznačnadifuzíâ AT skorohodav míroznačnadifuzíâ |