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Stochastic differential equations driven by stable processes for which pathwise uniqueness fails

Author

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  • Bass, Richard F.
  • Burdzy, Krzysztof
  • Chen, Zhen-Qing

Abstract

Let Zt be a one-dimensional symmetric stable process of order [alpha] with [alpha][set membership, variant](0,2) and consider the stochastic differential equationdXt=[phi](Xt-) dZt.For [beta]

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:1:p:1-15
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    Cited by:

    1. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    2. 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.
    3. Liang, Mingjie & Wang, Jian, 2020. "Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3053-3094.

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