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

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  • Xie, Longjie

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.

Suggested Citation

  • Xie, Longjie, 2017. "Singular SDEs with critical non-local and non-symmetric Lévy type generator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3792-3824.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:11:p:3792-3824
    DOI: 10.1016/j.spa.2017.03.014
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    References listed on IDEAS

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    1. Kim, Panki & Song, Renming & Vondraček, Zoran, 2014. "Global uniform boundary Harnack principle with explicit decay rate and its application," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 235-267.
    2. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    3. Bass, Richard F. & Burdzy, Krzysztof & Chen, Zhen-Qing, 2004. "Stochastic differential equations driven by stable processes for which pathwise uniqueness fails," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 1-15, May.
    4. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    5. Zhang, Xicheng, 2005. "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1805-1818, November.
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