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Probabilistic approach for semi-linear stochastic fractal equations

Author

Listed:
  • Xie, Yingchao
  • Zhang, Qi
  • Zhang, Xicheng

Abstract

In this work we provide a stochastic representation for a class of semi-linear stochastic fractal equations, and prove the existence and uniqueness of Wρ1,p-solutions to stochastic fractal equations by using purely probabilistic argument, where ρ is a suitable weighted function, and Wρ1,p is the associated first order weighted Sobolev space.

Suggested Citation

  • Xie, Yingchao & Zhang, Qi & Zhang, Xicheng, 2014. "Probabilistic approach for semi-linear stochastic fractal equations," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3948-3964.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:3948-3964
    DOI: 10.1016/j.spa.2014.07.007
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    References listed on IDEAS

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    1. Zhang, Xicheng, 2013. "Derivative formulas and gradient estimates for SDEs driven by α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1213-1228.
    2. Mikulevicius, R. & Pragarauskas, H., 2009. "On Hölder solutions of the integro-differential Zakai equation," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3319-3355, October.
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