# On the central limit theorem in Hilbert space.

Stochastica (1980)

- Volume: 4, Issue: 1, page 43-71
- ISSN: 0210-7821

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topGiné, 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 -

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