On the central limit theorem in Hilbert space.

Giné, Evarist, and León, José R.. "On the central limit theorem in Hilbert space.." Stochastica 4.1 (1980): 43-71. <http://eudml.org/doc/38833>.

@article{Giné1980,
abstract = {The object of this paper is to prove a central limit theorem in (separable) Hilbert space using a method based on the so called découpage de Lévy, the Lindeberg proof for the Gaussian case and an elementary proof of Poisson convergence for the direct part, and on elementary probabilistic inequalities for the converse. In particular, characteristic functions are only used in unicity questions. Several results of Varadhan (1962) can be obtained either directly as corollaries of the main theorem or with the same methods.},
author = {Giné, Evarist, León, José R.},
journal = {Stochastica},
keywords = {Espacios de Hilbert; Teorema central del límite; central limit theorem in Hilbert space; central limit problem in general Banach spaces},
language = {eng},
number = {1},
pages = {43-71},
title = {On the central limit theorem in Hilbert space.},
url = {http://eudml.org/doc/38833},
volume = {4},
year = {1980},
}

TY - JOUR
AU - Giné, Evarist
AU - León, José R.
TI - On the central limit theorem in Hilbert space.
JO - Stochastica
PY - 1980
VL - 4
IS - 1
SP - 43
EP - 71
AB - The object of this paper is to prove a central limit theorem in (separable) Hilbert space using a method based on the so called découpage de Lévy, the Lindeberg proof for the Gaussian case and an elementary proof of Poisson convergence for the direct part, and on elementary probabilistic inequalities for the converse. In particular, characteristic functions are only used in unicity questions. Several results of Varadhan (1962) can be obtained either directly as corollaries of the main theorem or with the same methods.
LA - eng
KW - Espacios de Hilbert; Teorema central del límite; central limit theorem in Hilbert space; central limit problem in general Banach spaces
UR - http://eudml.org/doc/38833
ER -