Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 457-467
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Yu. A. Davydov. The limit theorems for some functionals of processes with independent increments. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 457-467. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a1/
@article{TVP_1973_18_3_a1,
author = {Yu. A. Davydov},
title = {The limit theorems for some functionals of processes with independent increments},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {457--467},
year = {1973},
volume = {18},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a1/}
}
TY - JOUR
AU - Yu. A. Davydov
TI - The limit theorems for some functionals of processes with independent increments
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1973
SP - 457
EP - 467
VL - 18
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a1/
LA - ru
ID - TVP_1973_18_3_a1
ER -
%0 Journal Article
%A Yu. A. Davydov
%T The limit theorems for some functionals of processes with independent increments
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 457-467
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a1/
%G ru
%F TVP_1973_18_3_a1
This paper deals with asymptotical behaviour of the distribution of the functional $\frac1{D_T}\int_0^Th(S_t)\,dt$, where $S_t$ is a stochastic process with independent and stationary increments, $h(x)$ is a bounded function such that $$ \frac1{T^\beta}\int_0^Th(x)\,dx\to p,\quad\frac1{T^\beta}\int_{-T}^0h(x)\,dx\ge q,\quad T\to\infty,\quad0\le\beta\le1 $$ and $D_T$ is a normalizing factor.
