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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