On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$
UDC 519.21 We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in $L_{d+1}(R^{d+1}).$Actually, the powers of summability of the drift in $x$ and $t$ could be different. Our results seem to be new even if the diffusion is constant....
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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2020
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6280 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 519.21
We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in $L_{d+1}(R^{d+1}).$Actually, the powers of summability of the drift in $x$ and $t$ could be different. Our results seem to be new even if the diffusion is constant. The method of proving the solvability belongs to A. V. Skorokhod.Weak uniqueness of solutions is an open problem even if the diffusion is constant. |
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| DOI: | 10.37863/umzh.v72i9.6280 |