- Juan Jimenez
- University of Ottawa, CA
- Date: Apr. 17, Wednesday, 2024
- Time: 10:00am -- 10:50am
- Host: Le Chen
- Room: Parker 328
- Abstract: In recent years, a new class of processes became increasingly used as models for the noise in stochastic analysis, namely the Lévy processes. Since a Lévy process may be heavy-tailed, Lévy-based models have numerous applications in finance, risk theory, environmental studies, and physics. In this talk, I will explain how to show the existence and uniqueness of a solution for the non-linear stochastic wave equation in dimension \(d \le 2\), driven by a Lévy noise, using the past-light cone property of the fundamental solution. I consider a Lévy noise that may not have moments of any order higher than 2, such as the \(\alpha\)-stable Lévy noise. Secondly, I will show that the solution of the stochastic wave equation has bounded \(p\)-th moments up to a certain stopping time that depends on a compact region in \(\mathbb{R}^d\).