On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$

Abstract

We prove the solvability of Itô stochastic equations with uniformly nondegenerate, bounded, measurable diffusion and drift in $L_{d+1}({\mathbb{R}}^{d+1})$. Actually, the powers of summability of the drift in $x$ and $t$ could be different. Our results seem to be new even if the diffusion is constant. The method of proving the solvability belongs to A.V. Skorokhod. Weak uniqueness of solutions is an open problem even if the diffusion is constant.

22 pages, few glitches corrected, one reference added, several errors corrected