Singular SDEs with critical non-local and non-symmetric L\'evy type generator

Longjie Xie

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arXiv · 1610.07698

Singular SDEs with critical non-local and non-symmetric L\'evy type generator

Longjie Xie

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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.

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Longjie Xie. 2016-10-25. Singular SDEs with critical non-local and non-symmetric L\'evy type generator. https://arxiv.org/abs/1610.07698

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