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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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