On diffusion processes with drift in a Morrey class containing $L_{d+2}$

TL;DR

This paper introduces new conditions on the drift in Morrey spaces with mixed norms, enabling Aleksandrov type estimates for potentials of time-inhomogeneous diffusion processes in various function spaces.

Contribution

It provides novel drift conditions in Morrey spaces that facilitate potential estimates for complex diffusion processes.

Findings

Derived Aleksandrov type estimates for diffusion potentials.

Established drift conditions in Morrey spaces with mixed norms.

Extended results to spaces like $L_{d_{0}+1}$ with $d_{0}<d$.

Abstract

We present new conditions on the drift of the Morrey type with mixed norms allowing us to obtain Aleksandrov type estimates of potentials of time inhomogeneous diffusion processes in spaces with mixed norms and, for instance, in $L_{d_{0}+1}$ with $d_{0}<d$.