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Stochastic wave equation with heavy-tailed noise: Uniqueness of solutions and past light-cone property

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  • Jiménez, Juan J.

Abstract

In this article, we study the stochastic wave equation in spatial dimensions d≤2 with multiplicative Lévy noise that can have infinite pth moments. Using the past light-cone property of the wave equation, we prove the existence and uniqueness of a solution, considering only the p-integrability of the Lévy measure ν for the region corresponding to the small jumps of the noise. For d=1, there are no restrictions on ν. For d=2, we assume that there exists a value p∈(0,2) for which ∫{|z|≤1}|z|pν(dz)<+∞.

Suggested Citation

  • Jiménez, Juan J., 2024. "Stochastic wave equation with heavy-tailed noise: Uniqueness of solutions and past light-cone property," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001856
    DOI: 10.1016/j.spa.2024.104479
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    References listed on IDEAS

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    1. Chong, Carsten, 2017. "Stochastic PDEs with heavy-tailed noise," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2262-2280.
    2. Raluca M. Balan, 2014. "SPDEs with -Stable Lévy Noise: A Random Field Approach," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-22, February.
    3. Carsten Chong, 2017. "Lévy-driven Volterra Equations in Space and Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1014-1058, September.
    4. Raluca M. Balan & Cheikh B. Ndongo, 2017. "Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise," International Journal of Stochastic Analysis, Hindawi, vol. 2017, pages 1-9, March.
    5. 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.
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