Stochastic wave equation with Lévy white noise

Abstract

In this article, we study the stochastic wave equation on the entire space R d , driven by a space-time Lévy white noise with possibly infinite variance (such as the α-stable Lévy noise). In this equation, the noise is multiplied by a Lipschitz function σ(u) of the solution. We assume that the spatial dimension is d = 1 or d = 2. Under general conditions on the Lévy measure of the noise, we prove the existence of the solution, and we show that, as a function-valued process, the solution has a càdlàg modification in the local fractional Sobolev space of order r < 1/4 if d = 1, respectively r < −1 if d = 2.

Research on High-Speed Catamaran Motion Reduction with Semi-Active Control of Flexible Pontoon

“…In fact, it can be assumed that the main disturbance input to the system is the vertical displacement input of the wave, which can be simulated without a loss of generality by assuming randomly filtered white noise to simulate the vertical displacement of the wave [25].…”