Strong solutions of stochastic differential equations with square integrable drift
We prove the existence and uniqueness of strong solutions for stochastic differential equations in which the drift coefficient is square integrable in time variable and H\"{o}lder continuous in space variable. Moreover, we prove that the unique strong solution has a continuous modification, whi...
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Published in | arXiv.org |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
04.01.2021
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Subjects | |
Online Access | Get full text |
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Summary: | We prove the existence and uniqueness of strong solutions for stochastic differential equations in which the drift coefficient is square integrable in time variable and H\"{o}lder continuous in space variable. Moreover, we prove that the unique strong solution has a continuous modification, which is \(\beta\)-H\"{o}lder continuous in space variable for every \(\beta\in (0,1)\), and as an \(L^2(\Omega\times (0,T))\) valued function, it is differentiable as well. |
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ISSN: | 2331-8422 |