Stochastic differential equations with critical drifts

Kyeongsik Nam

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5366-5393

Abstract: 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 Lq,1([0,T],Lxp) for p,q∈(1,∞) satisfying 2q+dp=1, then the corresponding SDE admits a unique strong solution. We also derive the Sobolev regularity of a solution under the Orlicz-critical condition.

Keywords: Stochastic differential equations; Lorentz spaces (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.03.010

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