Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes

Let $\theta$ be a short memory shot noise process. For wide classes of “stochastically Lipschitzian” (SL) and “stochastically locally Lipschitzian” (SLL) non-linear functions $K\colon{\mathbb R}\to{\mathbb R}$, we prove asymptotic normality of the normalized integrals $\Theta_K(T)=\int_0^TK(\theta(t))\,dt$ as $T\to\infty$. We also consider various examples of SL and SLL functions.