On Measure-Valued Processes Generated by Differential Equations
We study the problem of representation of a homogeneous semigroup {Θ t } t ≥ 0 of transformations of probability measures on \(\mathbb{R}^d \) in the form \(\Theta _t (\mu) = \mu \circ u_{\mu}^{-1} (\cdot ,t),\) where \(u_{\mu} :\mathbb{R}^d \times [0, T] \to \mathbb{R}^d\) satisfies a d...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3925 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510055955169280 |
|---|---|
| author | Feshchenko, O. Yu. Фещенко, О. Ю. |
| author_facet | Feshchenko, O. Yu. Фещенко, О. Ю. |
| author_sort | Feshchenko, O. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:15:31Z |
| description | We study the problem of representation of a homogeneous semigroup {Θ t } t ≥ 0 of transformations of probability measures on \(\mathbb{R}^d \) in the form \(\Theta _t (\mu) = \mu \circ u_{\mu}^{-1} (\cdot ,t),\) where \(u_{\mu} :\mathbb{R}^d \times [0, T] \to \mathbb{R}^d\) satisfies a differential equation of a special form dependent on the measure μ. We give necessary and sufficient conditions for this representation. |
| first_indexed | 2026-03-24T02:50:55Z |
| format | Article |
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| id | umjimathkievua-article-3925 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:50:55Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8a/c45f4e9b1a8fd6aaf24937499179e88a.pdf |
| spelling | umjimathkievua-article-39252020-03-18T20:15:31Z On Measure-Valued Processes Generated by Differential Equations Про мірозначні процеси, породжені диференціальними рівняннями Feshchenko, O. Yu. Фещенко, О. Ю. We study the problem of representation of a homogeneous semigroup {Θ t } t ≥ 0 of transformations of probability measures on \(\mathbb{R}^d \) in the form \(\Theta _t (\mu) = \mu \circ u_{\mu}^{-1} (\cdot ,t),\) where \(u_{\mu} :\mathbb{R}^d \times [0, T] \to \mathbb{R}^d\) satisfies a differential equation of a special form dependent on the measure μ. We give necessary and sufficient conditions for this representation. Вивчається питання зображення однорідної напівгрупи $\{Θ_t\}t ≥ 0$ перетворень імовірнісних мір на $R^d$ у вигляді $\Theta _t (\mu) = \mu \circ u_{\mu}^{-1} (\cdot ,t),$ де $u_{\mu} :\mathbb{R}^d \times [0, T] \to \mathbb{R}^d$ задовольняє диференціальне рівняння спеціального вигляду, що залежить від міри $μ$. Наводяться необхідні і достатні умови такого зображення. Institute of Mathematics, NAS of Ukraine 2003-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3925 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 4 (2003); 525-532 Український математичний журнал; Том 55 № 4 (2003); 525-532 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3925/4564 https://umj.imath.kiev.ua/index.php/umj/article/view/3925/4565 Copyright (c) 2003 Feshchenko O. Yu. |
| spellingShingle | Feshchenko, O. Yu. Фещенко, О. Ю. On Measure-Valued Processes Generated by Differential Equations |
| title | On Measure-Valued Processes Generated by Differential Equations |
| title_alt | Про мірозначні процеси, породжені диференціальними рівняннями |
| title_full | On Measure-Valued Processes Generated by Differential Equations |
| title_fullStr | On Measure-Valued Processes Generated by Differential Equations |
| title_full_unstemmed | On Measure-Valued Processes Generated by Differential Equations |
| title_short | On Measure-Valued Processes Generated by Differential Equations |
| title_sort | on measure-valued processes generated by differential equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3925 |
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