Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes
Andrii B. Ilienko, Josef G. SteinebachTheory 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
Θ_{K}(T) = | T ⌠ ⌡ 0 |
K(θ(t)) dt |