DMS Analysis and Stochastic Analysis Seminar (SASA)

Time: Apr 24, 2024 (10:00 AM)
Location: 328 Parker Hall

Speaker: Juan Jimenez (University of Ottawa, Canada)
Title: Uniqueness of solutions for the stochastic wave equation driven by heavy-tailed Lévy noises
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 \(d<=2\), 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.