# Stochastic differential equations with critical drifts

@article{Nam2020StochasticDE,
title={Stochastic differential equations with critical drifts},
author={Kyeongsik Nam},
journal={Stochastic Processes and their Applications},
year={2020}
}
• Kyeongsik Nam
• Published 31 January 2018
• Mathematics
• Stochastic Processes and their Applications
We establish the well-posedness of SDE with the additive noise when a singular drift belongs to the critical spaces. We prove that if the drift belongs to the Orlicz-critical space $L^{q,1}([0,T],L^p_x)$ for $p,q\in (1,\infty)$ satisfying $\frac{2}{q}+\frac{d}{p} =1$, then the corresponding SDE admits a unique strong solution. We also derive the Sobolev regularity of a solution under the Orlicz-critical condition.
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