Singular SDEs with critical non-local and non-symmetric L\'evy type generator
Probability
2016-10-26 v1 Analysis of PDEs
Abstract
In this work, by using Levi's parametrix method we first construct the fundamental solution of the critical non-local operator perturbed by gradient. Then, we use the obtained estimates to prove the existence and uniqueness of strong solutions for stochastic differential equation driven by Markov process with irregular coefficients, whose generator is a non-local and non-symmetric L\'evy type operator.
Keywords
Cite
@article{arxiv.1610.07698,
title = {Singular SDEs with critical non-local and non-symmetric L\'evy type generator},
author = {Longjie Xie},
journal= {arXiv preprint arXiv:1610.07698},
year = {2016}
}