Almost sure CLT for hyperbolic Anderson model with L\'evy colored noise

Abstract

In this note, we prove the Almost Sure Central Limit Theorem (ASCLT) for the spatial integral of the solution of the hyperbolic Anderson model driven by the L\'evy colored noise introduced in Balan (2015). For this, we use the central limit theorem for the normalized spatial integral, and an estimate for the Malliavin derivative of the solution, both derived in the recent preprint Balan and Stephenson (2026). We assume that the spatial correlation kernel of the noise is either integrable, or it is given by the Riesz kernel.