Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 75-93
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I. A. Ibragimov. On a hitting probability of Gaussian random vector into a small ball in a Hilbert space. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 75-93. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a5/
@article{ZNSL_1979_85_a5,
author = {I. A. Ibragimov},
title = {On a~hitting probability of {Gaussian} random vector into a~small ball in {a~Hilbert} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {75--93},
year = {1979},
volume = {85},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a5/}
}
TY - JOUR
AU - I. A. Ibragimov
TI - On a hitting probability of Gaussian random vector into a small ball in a Hilbert space
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 75
EP - 93
VL - 85
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a5/
LA - ru
ID - ZNSL_1979_85_a5
ER -
%0 Journal Article
%A I. A. Ibragimov
%T On a hitting probability of Gaussian random vector into a small ball in a Hilbert space
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 75-93
%V 85
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a5/
%G ru
%F ZNSL_1979_85_a5
Let $\xi$ be a Gaussian random vector taking its value in a Hilbert space $H$. Denote by $\theta(a,z)$ the ball in $H$ with center $a$ and radius $z$. Let $I(a,z)=\Prob\{\xi\in\theta(a,z)\}$, $z\to0$. We give some asymptotic formulas for $I(a,z)$ valid when $z\to0$.
