For Itô stochastic processes in ${\mathbb{R}}^d$ with drift in $L_d$ Aleksandrov’s type estimates are established in the elliptic and parabolic settings. They are applied to estimating the resolvent operators of the corresponding elliptic and parabolic operators in $L_p$ and $L_{p+1}$, respectively, where $p\ge d$.

中文翻译：

---

在随机的Itô过程中 ${\mathrm{大号}}_d$

对于Itô的随机过程 ${\mathbb{[R}}^d$ 随着漂移 ${\mathrm{大号}}_d$Aleksandrov的类型估计是在椭圆和抛物线环境中建立的。它们被用于估计相应的椭圆和抛物线算子的分解算子。${\mathrm{大号}}_p$ 和 ${\mathrm{大号}}_{p+\mathrm{1个}}$分别在哪里 $p\ge d$。