Stochastic equations with time-dependent singular drift

We prove unique weak solvability and Feller property for stochastic differential equations with drift in a large class of time-dependent vector fields. This class contains, in particular, the critical Ladyzhenskaya-Prodi-Serrin class, the weak $L^d$ class as well as some vector fields that are not even in $L^{2+\varepsilon}_{\rm loc}$, $\varepsilon>0$.

STOCHASTIC EQUATIONS WITH TIME-DEPENDENT SINGULAR DRIFT D. KINZEBULATOV AND K.R. MADOU Abstract. We prove unique weak solvability for stochastic differential equations with drift arXiv:2105.07312v2 [math.PR] 19 Oct 2021 in a large class of time-dependent vector fields. This class contains, in particular, the critical Ladyzhenskaya-Prodi-Serrin class, the…

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