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

Juan J. Jiménez

Stochastic Processes and their Applications, 2024, vol. 178, issue C

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)<+∞.

Keywords: Stochastic partial differential equations; Random fields; Space–time Lévy white noise (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104479

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