Singular SDEs with critical non-local and non-symmetric Lévy type generator

Longjie Xie

Stochastic Processes and their Applications, 2017, vol. 127, issue 11, 3792-3824

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 pathwise uniqueness of strong solutions for stochastic differential equation driven by Markov process with irregular coefficients, whose generator is a non-local and non-symmetric Lévy type operator.

Keywords: Fundamental solution; Non-local operator; Pathwise uniqueness; Singular SDEs (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:11:p:3792-3824

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DOI: 10.1016/j.spa.2017.03.014

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