Central limit theorems in Hölder topologies

A. Račkauskas   ; Ch. Suquet

Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 109-125

Résumé

For rather general moduli of smoothness $\rho$, such as $\rho(h)=h^\alpha \log^\beta (c/h)$, we consider the Hölder spaces $H_{\rho}(B)$ of functions $[0,1]^d \to B$, where $B$ is a separable Banach space. Using isomorphism between $H_{\rho}(B)$ and some sequence Banach space we follow a very natural way to study, in terms of second differences, the central limit theorem for independent identically distributed sequences of random elements in $H_{\rho}(B)$.

Détail

Keywords: Banach valued Brownian motion, central limit theorem, Rosenthal inequality, second difference, skew pyramidal basis, tightness, type 2 space.
Mots-clés : Schauder decomposition

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