Displaying similar documents to “Central limit problem and invariance principles on Banach spaces”

On the central limit theorem in Hilbert space.

Evarist Giné, José R. León (1980)

Stochastica

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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...

Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences

Jérôme Dedecker, Sana Louhichi (2005)

ESAIM: Probability and Statistics

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We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit....