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A Zvonkin's transformation for stochastic differential equations with singular drift and applications
Journal of Differential Equations, Volume: 297, Pages: 277 - 319
Swansea University Author:
Chenggui Yuan
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DOI (Published version): 10.1016/j.jde.2021.06.031
Abstract
In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz fi...
| Published in: | Journal of Differential Equations |
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| ISSN: | 0022-0396 |
| Published: |
Elsevier BV
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa57821 |
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| Abstract: |
In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with H\"older continuous diffusion coefficient and singular drift term without regularity assumption. |
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| Keywords: |
Zvonkin's transformation; singular diffusion processes; Krylov's estimate; Harnack inequality |
| College: |
Faculty of Science and Engineering |
| Start Page: |
277 |
| End Page: |
319 |