On weak and strong solutions of time inhomogeneous Itô's equations with VMO diffusion and Morrey drift

Abstract

We prove the existence of weak solutions of Itô's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Weak uniqueness (generally conditional) and a conjecture pertaining to strong solutions are also discussed. Our results are new even if the drift term vanishes.

36 pages. arXiv admin note: substantial text overlap with arXiv:2206.07871, some assertions are made stronger for later use, just cosmetic changes requested by referees of the previous version