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

Andrii B. Ilienko, Josef G. Steinebach
Theory of Stochastic Processes
Vol.17 (33), no.2, 2011, pp.25-34
Let θ be a short memory shot noise process. For wide classes of "stochastically Lipschitzian" (SL) and "stochastically locally Lipschitzian" (SLL) non-linear functions K: R → R, we prove asymptotic normality of the normalized integrals

ΘK(T) =

T ⌠ ⌡ 0

K(θ(t)) dt

as T → ∞. We also consider various examples of SL and SLL functions.