On stochastic equations with drift in $L_{d}$
Probability
2020-09-03 v3
Abstract
For It\^o stochastic equations in with drift in several results are discussed such as the existence of weak solutions, the existence of the corresponding Markov process, Aleksandrov type estimates of their Green's functions, which yield their summability to the power of , the Fabes-Stroock type estimates which show that Green's functions are summable to a higher degree, the Fanghua Lin type estimates, which are one of the main tools in the -theory of fully nonlinear elliptic equations, the fact that Green's functions are in the class of Muckenhoupt and a few other results.
Cite
@article{arxiv.2001.04008,
title = {On stochastic equations with drift in $L_{d}$},
author = {N. V. Krylov},
journal= {arXiv preprint arXiv:2001.04008},
year = {2020}
}
Comments
31 pages, one remark rewritten, numerous misprints corrected, a reference updated, Theorem 2.6 is corrected