Functional limit theorems for a time-changed multidimensional Wiener process
UDC 519.21 We study the asymptotic behavior of a properly normalized time-changed multidimensional Wiener process. The time change is described by an additive (in time) functional of the Wiener process itself. On the level of generators, the time change means that we consider the Laplace operator, w...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8981 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1862133841062264832 |
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| author | Mishura, Yuliya Schilling, René L. Mishura, Yuliya Schilling, René L. |
| author_facet | Mishura, Yuliya Schilling, René L. Mishura, Yuliya Schilling, René L. |
| author_sort | Mishura, Yuliya |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-04-10T12:36:03Z |
| description | UDC 519.21
We study the asymptotic behavior of a properly normalized time-changed multidimensional Wiener process. The time change is described by an additive (in time) functional of the Wiener process itself. On the level of generators, the time change means that we consider the Laplace operator, which generates a multidimensional Wiener process, and multiply it by a (possibly degenerate) state-space dependent intensity. It is assumed that the intensity admits limits at infinity in each octant of the state space but the values of these limits may be different. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time-changed multidimensional Wiener process. Among possible limits, there is a multidimensional analog of the skew Brownian motion. |
| doi_str_mv | 10.3842/umzh.v77i4.8981 |
| first_indexed | 2026-03-24T03:43:16Z |
| format | Article |
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| id | umjimathkievua-article-8981 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-11T01:00:17Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-89812026-04-10T12:36:03Z Functional limit theorems for a time-changed multidimensional Wiener process Functional limit theorems for a time-changed multidimensional Wiener process Mishura, Yuliya Schilling, René L. Mishura, Yuliya Schilling, René L. Multidimensional Wiener process; time change; functional limit theorem; multidimensional skew Brownian motion UDC 519.21 We study the asymptotic behavior of a properly normalized time-changed multidimensional Wiener process. The time change is described by an additive (in time) functional of the Wiener process itself. On the level of generators, the time change means that we consider the Laplace operator, which generates a multidimensional Wiener process, and multiply it by a (possibly degenerate) state-space dependent intensity. It is assumed that the intensity admits limits at infinity in each octant of the state space but the values of these limits may be different. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time-changed multidimensional Wiener process. Among possible limits, there is a multidimensional analog of the skew Brownian motion. УДК 519.21 Функціональні граничні теореми для багатовимірного процесу Вінера, що змінюється у часі Досліджено асимптотичну поведінку належним чином нормованого багатовимірного процесу Вінера з часовою зміною. Часову зміну описано адитивним (за часом) функціоналом самого процесу Вінера. На рівні генераторів зміна часу означає, що розглянуто оператор Лапласа, який породжує багатовимірний процес Вінера, помножений на (можливо, вироджену) інтенсивність, що залежить від стану. Припущено, що ця інтенсивність має границі на нескінченності в кожному октанті простору станів, причому значення цих границь можуть відрізнятися. Із застосуванням функціональних граничних теорем для суперпозиції стохастичних процесів доведено функціональні граничні теореми для нормованого багатовимірного процесу Вінера зі зміною в часі. Серед можливих граничних процесів існує багатовимірний аналог кососиметричного броунівського руху. Institute of Mathematics, NAS of Ukraine 2026-04-10 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8981 10.3842/umzh.v77i4.8981 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 4 (2025); 289–290 Український математичний журнал; Том 77 № 4 (2025); 289–290 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8981/10447 Copyright (c) 2025 Yuliya Mishura, René L. Schilling |
| spellingShingle | Mishura, Yuliya Schilling, René L. Mishura, Yuliya Schilling, René L. Functional limit theorems for a time-changed multidimensional Wiener process |
| title | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_alt | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_full | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_fullStr | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_full_unstemmed | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_short | Functional limit theorems for a time-changed multidimensional Wiener process |
| title_sort | functional limit theorems for a time-changed multidimensional wiener process |
| topic_facet | Multidimensional Wiener process time change functional limit theorem multidimensional skew Brownian motion |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8981 |
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