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

N. V.  Krylov

doi:10.37863/umzh.v72i9.6280

N. V. Krylov Univ. Minnesota, Minneapolis, MN, USA

DOI: https://doi.org/10.37863/umzh.v72i9.6280

Keywords: Itˆo’s equations with singular drift, Markov diffusion processes

Abstract

UDC 519.21

We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in $L_{d+1}(R^{d+1}).$
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.

Author Biography

N. V. Krylov, Univ. Minnesota, Minneapolis, MN, USA

Univ. Minnesota, Minneapolis, MN, USA

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