On the small mass limit of stochastic wave equation driven by cylindrical stable process

We explore the small mass limit of a stochastic wave equation (SWE) driven by cylindrical α-stable noise, where α ∈ (1, 2), and prove that it converges to a stochastic heat equation. Using a splitting technique, we decompose the velocity component into three parts, which gives convenience to the moment estimate. We show the tightness of solution of SWE in SM 1 topology. After these preparation, we pass the limit and derive the approximation equation.