On strong solutions of time inhomogeneous It\^o's equations with "supercritical" diffusion and drift

TL;DR

This paper establishes strong existence and uniqueness for time-inhomogeneous Itô equations with irregular, supercritical diffusion and drift terms, advancing the understanding of stochastic differential equations with challenging coefficients.

Contribution

It introduces methods to prove strong solutions for supercritical Itô equations with irregular coefficients, a case previously less understood.

Findings

Proved strong existence and uniqueness under supercritical conditions.

Extended the theory to irregular diffusion and drift of Morrey class.

Addressed a challenging class of stochastic equations with irregular coefficients.

Abstract

We prove strong existence and uniqueness of solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class type. In a sense we are treating a "supercritical" case.