Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 83-87
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A. Yu. Zaitsev. The estimation of proximity of distribution of sequential sums of independent identically distributed random vectors. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 83-87. http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a8/
@article{ZNSL_1980_97_a8,
author = {A. Yu. Zaitsev},
title = {The estimation of proximity of distribution of sequential sums of independent identically distributed random vectors},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {83--87},
year = {1980},
volume = {97},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a8/}
}
TY - JOUR
AU - A. Yu. Zaitsev
TI - The estimation of proximity of distribution of sequential sums of independent identically distributed random vectors
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1980
SP - 83
EP - 87
VL - 97
UR - http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a8/
LA - ru
ID - ZNSL_1980_97_a8
ER -
%0 Journal Article
%A A. Yu. Zaitsev
%T The estimation of proximity of distribution of sequential sums of independent identically distributed random vectors
%J Zapiski Nauchnykh Seminarov POMI
%D 1980
%P 83-87
%V 97
%U http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a8/
%G ru
%F ZNSL_1980_97_a8
Let $F$ be a distribution on $\mathbb R^k$, $F_k^n$ – times convolution of $F$ with itself, $\mathscr L^k=\{B\in\mathbb R^k,B=[a_1,b_1]\times\dots\times[a_k,b_k]\}$. It is proved that $$ \sup_{B\in\mathscr L^k}|F^{n+1}\{B\}-F^n\{B\}|\le\frac{c(F)}{\sqrt n}, $$ where $c(F)$ depends on some characteristics of $F$.
