Once again about weak uniqueness for SDE with singular coefficients

TL;DR

This paper establishes weak uniqueness for solutions of Itô's stochastic differential equations with certain irregular coefficients, extending the class of coefficients for which uniqueness holds.

Contribution

It introduces new conditions on the coefficients, including near-VMO and Morrey class functions, to prove weak uniqueness for SDEs with singular coefficients.

Findings

Weak uniqueness holds for SDEs with almost VMO diffusion coefficients.

Solutions are admissible when the drift is in L_d.

The results extend the class of coefficients ensuring uniqueness.

Abstract

We prove weak uniqueness for admissible solutions of It\^o's equations with uniformly nondegenerate $a$ which is almost in VMO and $b$ in a Morrey class of functions with low integrability property. If $b\in L_{d}$ any solution is admissible.