On stochastic Itô processes with drift in $L_d$

Abstract

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 $p\ge d$.

27 pages, some misprints are corrected, references added

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