Some properties of solutions of Itô equations with drift in $L_{d+1}$

Abstract

This paper is a natural continuation of [8], where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}({\mathbb{R}}^{d+1})$. Here we study some properties of these processes such as higher summability of Green's functions, boundedness of resolvent operators in Lebesgue spaces, establish Itô's formula, and so on.

26 pages, part of the previous paper is deleted because of not enough arguments