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.

arXiv comment22 pages, few glitches corrected, one reference added, several errors corrected

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Cited by in corpus (3)

• SDEs with critical time dependent drifts: weak solutions
• Stochastic transport equation with singular drift
• Maximum principle for non-uniformly parabolic equations and applications