Heat equation with a general stochastic measure in a bounded domain
A stochastic heat equation on $[0,T]\times B$, where B is a bounded domain, is considered. The equation is driven by a general stochastic measure, for which only σ-additivity in probability is assumed. The existence, uniqueness and Hölder regularity of the solution are proved.
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| Format: | Article |
| Language: | English |
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VTeX
2024-07-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/24-VMSTA262 |
| _version_ | 1826883613900144640 |
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| author | Boris Manikin |
| author_facet | Boris Manikin |
| author_sort | Boris Manikin |
| collection | DOAJ |
| description | A stochastic heat equation on $[0,T]\times B$, where B is a bounded domain, is considered. The equation is driven by a general stochastic measure, for which only σ-additivity in probability is assumed. The existence, uniqueness and Hölder regularity of the solution are proved. |
| first_indexed | 2025-02-17T03:51:21Z |
| format | Article |
| id | doaj.art-7ad607ceb0ef48a8b9d21f8054cc296d |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2025-02-17T03:51:21Z |
| publishDate | 2024-07-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-7ad607ceb0ef48a8b9d21f8054cc296d2025-01-10T11:16:09ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542024-07-01121618210.15559/24-VMSTA262Heat equation with a general stochastic measure in a bounded domainBoris Manikin0Taras Shevchenko National University of Kyiv, Kyiv, UkraineA stochastic heat equation on $[0,T]\times B$, where B is a bounded domain, is considered. The equation is driven by a general stochastic measure, for which only σ-additivity in probability is assumed. The existence, uniqueness and Hölder regularity of the solution are proved.https://www.vmsta.org/doi/10.15559/24-VMSTA262Heat equationmild solutionStochastic measureHölder regularity |
| spellingShingle | Boris Manikin Heat equation with a general stochastic measure in a bounded domain Modern Stochastics: Theory and Applications Heat equation mild solution Stochastic measure Hölder regularity |
| title | Heat equation with a general stochastic measure in a bounded domain |
| title_full | Heat equation with a general stochastic measure in a bounded domain |
| title_fullStr | Heat equation with a general stochastic measure in a bounded domain |
| title_full_unstemmed | Heat equation with a general stochastic measure in a bounded domain |
| title_short | Heat equation with a general stochastic measure in a bounded domain |
| title_sort | heat equation with a general stochastic measure in a bounded domain |
| topic | Heat equation mild solution Stochastic measure Hölder regularity |
| url | https://www.vmsta.org/doi/10.15559/24-VMSTA262 |
| work_keys_str_mv | AT borismanikin heatequationwithageneralstochasticmeasureinaboundeddomain |