Limit theorems for diffusion-type processes in $R^m$
For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures $\mu _{(\xi ^{(n)} ,w)},\; n = 1, ... ,$ associated with the solutions, to the limiting measure $\mu _{(\xi ^{(0)} ,w)}$. The co...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5942 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512166857146368 |
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| author | Pisanets, S. I. Писанец, С. И. Писанец, С. И. |
| author_facet | Pisanets, S. I. Писанец, С. И. Писанец, С. И. |
| author_sort | Pisanets, S. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:21:43Z |
| description | For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures $\mu _{(\xi ^{(n)} ,w)},\; n = 1, ... ,$ associated with the solutions, to the limiting measure $\mu _{(\xi ^{(0)} ,w)}$. The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well. |
| first_indexed | 2026-03-24T03:24:28Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5942 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:28Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/97/ed1428e55ce1eeb7ed5df22531d80797.pdf |
| spelling | umjimathkievua-article-59422020-03-19T09:21:43Z Limit theorems for diffusion-type processes in $R^m$ Несколько предельных теорем для процессов диффузионного типа в $R^m$ Pisanets, S. I. Писанец, С. И. Писанец, С. И. For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures $\mu _{(\xi ^{(n)} ,w)},\; n = 1, ... ,$ associated with the solutions, to the limiting measure $\mu _{(\xi ^{(0)} ,w)}$. The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well. Для послідовності стохастичиих рівнянь дифузійного типу знайдені умови, близькі до необхідних і достатніх, для слабкої збіжності мір $\mu _{(\xi ^{(n)} ,w)},\; n = 1, ... ,$ відповідають розв'язкам, до граничної а також умови $\mu _{(\xi ^{(0)} ,w)}$, при виконанні яких із слабкої збіжності розв’язків стохастичних рівнянь випливає сильна збіжність. Institute of Mathematics, NAS of Ukraine 1993-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5942 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 10 (1993); 1371–1378 Український математичний журнал; Том 45 № 10 (1993); 1371–1378 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5942/8567 https://umj.imath.kiev.ua/index.php/umj/article/view/5942/8568 Copyright (c) 1993 Pisanets S. I. |
| spellingShingle | Pisanets, S. I. Писанец, С. И. Писанец, С. И. Limit theorems for diffusion-type processes in $R^m$ |
| title | Limit theorems for diffusion-type processes in $R^m$ |
| title_alt | Несколько предельных теорем для процессов диффузионного типа в $R^m$ |
| title_full | Limit theorems for diffusion-type processes in $R^m$ |
| title_fullStr | Limit theorems for diffusion-type processes in $R^m$ |
| title_full_unstemmed | Limit theorems for diffusion-type processes in $R^m$ |
| title_short | Limit theorems for diffusion-type processes in $R^m$ |
| title_sort | limit theorems for diffusion-type processes in $r^m$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5942 |
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