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Intermittency for the wave equation with Lévy white noise

Author

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  • Balan, Raluca M.
  • Ndongo, Cheikh B.

Abstract

In this article, we consider the stochastic wave equation on R+×R driven by the Lévy white noise introduced in Balan (2015). Using Rosenthal’s inequality, we develop a maximal inequality for the moments of order p≥2 of the integral with respect to this noise. Based on this inequality, we show that this equation has a unique solution, which is weakly intermittent in the sense of Foondun and Khoshnevisan (2009) and Khoshnevisan (2014).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:214-223
    DOI: 10.1016/j.spl.2015.09.027
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    References listed on IDEAS

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    1. Fournier, Nicolas, 2000. "Malliavin calculus for parabolic SPDEs with jumps," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 115-147, May.
    2. Ren, Yao-Feng & Tian, Fan-Ji, 2003. "On the Rosenthal's inequality for locally square integrable martingales," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 107-116, March.
    3. 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.
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