On strong solutions of time inhomogeneous It\^o's equations with Morrey diffusion gradient and drift. A supercritical case

TL;DR

This paper establishes the existence and discusses the uniqueness of strong solutions for stochastic Itô equations with irregular, Morrey space-based diffusion and drift terms, particularly in supercritical cases.

Contribution

It introduces new methods to prove strong solutions for time-inhomogeneous Itô equations with Morrey space coefficients, addressing supercritical irregularities.

Findings

Existence of strong solutions under Morrey space conditions

Strong uniqueness results for irregular coefficients

Extension to supercritical cases with irregular diffusion and drift

Abstract

We prove the existence of strong solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Strong uniqueness is also discussed.