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Stochastic equations with low regularity drifts (2310.00421v2)
Published 30 Sep 2023 in math.PR
Abstract: By using the It^{o}-Tanaka trick, we prove the unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular drifts in low regularity Lebesgue-H\"{o}lder space $Lq(0,T;{\mathcal C}_b\alpha({\mathbb R}d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$). As applications, we show the unique weak and strong solvability for stochastic transport equations driven by the low regularity drift with $q\in (4/(2+\alpha),2$) as well as the local Lipschitz estimate for stochastic strong solutions.