Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 119-152

Title MODERATE DEVIATION PRINCIPLE FOR STOCHASTIC WAVE EQUATIONS WITH A RANDOM DYNAMICAL BOUNDARY DRIVEN BY MULTIPLICATIVE LÉVY NOISES

Author Ying Wang, Guanggan Chen and Pin Wang

(Received August 30, 2022, revised May 8, 2023)
Abstract. This work focuses on a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition driven by multiplicative Lévy noises. Since the Lévy jump noises disturbing and the singular perturbing not only affect the physical medium but also appear on its boundary, it seeks the convergence relations to balance the deviation scale and the singular perturbation and improve the regularity of the system. Employing the stochastic control argument, it derives the tightness of the system by constructing the equivalent form of the deviation system. Based on the weak convergence method and a splitting skill, it establishes a moderate deviation principle for this system.

Mathematics Subject Classification. Primary 60H15; Secondary 37L55, 35L05, 60F05.
Key words and phrases. Moderate deviation principle, Poisson random measure, random dynamical boundary condition, stochastic wave equation.

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