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On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension

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  • Debbi, Latifa
  • Dozzi, Marco

Abstract

Existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional nonlinear stochastic fractional partial differential equations of order [alpha]>1 containing derivatives of entire order and perturbed by space-time white noise are studied. The fractional derivative operator is defined by means of a generalized Riesz-Feller potential.

Suggested Citation

  • Debbi, Latifa & Dozzi, Marco, 2005. "On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1764-1781, November.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:11:p:1764-1781
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    References listed on IDEAS

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    1. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
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    Cited by:

    1. Junfeng Liu, 2023. "Moment Bounds for a Generalized Anderson Model with Gaussian Noise Rough in Space," Journal of Theoretical Probability, Springer, vol. 36(1), pages 167-200, March.
    2. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.
    3. Dalang, Robert C. & Pu, Fei, 2021. "Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 359-393.
    4. Yanmei Liu & Monzorul Khan & Yubin Yan, 2016. "Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations," Mathematics, MDPI, vol. 4(3), pages 1-28, July.
    5. Wu, Dongsheng, 2011. "On the solution process for a stochastic fractional partial differential equation driven by space-time white noise," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1161-1172, August.

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