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/}
}
TY - JOUR AU - Andrii B. Ilienko AU - Josef G. Steinebach TI - Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes JO - Teoriâ slučajnyh processov PY - 2011 SP - 25 EP - 34 VL - 17 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a2/ LA - en ID - THSP_2011_17_2_a2 ER -
%0 Journal Article %A Andrii B. Ilienko %A Josef G. Steinebach %T Stochastically Lipschitzian functions and limit theorems for functionals of shot noise processes %J Teoriâ slučajnyh processov %D 2011 %P 25-34 %V 17 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a2/ %G en %F THSP_2011_17_2_a2
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/