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Parabolic SPDEs driven by Poisson white noise

Author

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  • Albeverio, Sergio
  • Wu, Jiang-Lun
  • Zhang, Tu-Sheng

Abstract

Stochastic partial differential equations (SPDEs) of parabolic type driven by (pure) Poisson white noise are investigated in this paper. These equations are interpreted as stochastic integral equations of the jump type involving evolution kernels. Existence and uniqueness of the solution is established.

Suggested Citation

  • Albeverio, Sergio & Wu, Jiang-Lun & Zhang, Tu-Sheng, 1998. "Parabolic SPDEs driven by Poisson white noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 21-36, May.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:21-36
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    Citations

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    Cited by:

    1. Funaki, Tadahisa & Xie, Bin, 2009. "A stochastic heat equation with the distributions of Lévy processes as its invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 307-326, February.
    2. Seleši, Dora, 2011. "Fundamental solutions of singular SPDEs," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 526-537.
    3. Chong, Carsten, 2017. "Stochastic PDEs with heavy-tailed noise," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2262-2280.
    4. Balan, Raluca M. & Ndongo, Cheikh B., 2016. "Intermittency for the wave equation with Lévy white noise," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 214-223.
    5. Albeverio, S. & Mandrekar, V. & Rüdiger, B., 2009. "Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 835-863, March.
    6. Anh, V. V. & Leonenko, N. N., 1999. "Non-Gaussian scenarios for the heat equation with singular initial conditions," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 91-114, November.
    7. Carsten Chong, 2017. "Lévy-driven Volterra Equations in Space and Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1014-1058, September.
    8. Albeverio, Sergio & Mastrogiacomo, Elisa & Smii, Boubaker, 2013. "Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2084-2109.
    9. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2018. "Long time behavior for stochastic Burgers equations with jump noises," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 41-49.
    10. Xie, Yingchao, 2010. "Poincaré inequality for linear SPDE driven by Lévy Noise," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1950-1965, September.

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