English

Some properties of solutions of It\^o equations with drift in $L_{d+1}$

Probability 2020-12-24 v2

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 Ld+1(Rd+1)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 It\^o's formula, and so on.

Keywords

Cite

@article{arxiv.2011.04589,
  title  = {Some properties of solutions of It\^o equations with drift in $L_{d+1}$},
  author = {N. V. Krylov},
  journal= {arXiv preprint arXiv:2011.04589},
  year   = {2020}
}

Comments

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