THE CENTRAL-LIMIT-THEOREM FOR RANDOM PERTURBATIONS OF ROTATIONS

Authors
DENKER M GORDIN M
Citation
M. Denker et M. Gordin, THE CENTRAL-LIMIT-THEOREM FOR RANDOM PERTURBATIONS OF ROTATIONS, Probability theory and related fields, 111(1), 1998, pp. 1-16
Citations number
9
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Probability theory and related fields → ACNP
ISSN journal
01788051
Volume
111
Issue
1
Year of publication
1998
Pages
1 - 16
Database
ISI
SICI code
0178-8051(1998)111:1<1:TCFRPO>2.0.ZU;2-5
Abstract
We prove a functional central limit theorem for stationary random sequ ences given by the transformations T-epsilon,T-omega(x, y) = (2x, y omega + epsilon x) mod 1 on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary mar tingale differences with values in a separable Hilbert space of square integrable functions.