Geodesic
Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes
Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 25-34

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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.
Keywords: Shot noise process, non-linear function, integrated process, central limit theorem. 
@article{THSP_2011_17_2_a2,
     author = {Andrii B. Ilienko and Josef G. Steinebach},
     title = {Stochastically {Lipschitzian} functions and limit theorems for functionals of shot noise processes},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {25--34},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a2/}
}
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Andrii B. Ilienko; Josef G. Steinebach. Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes. Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 25-34. http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a2/