It is shown that if, for a piecewise $C^2$ mapping of the unit interval into itself where the absolute value of the derivative is greater than 1, an invariant measure is weak-mixing, then a central limit theorem holds for a class of real Holder functions.
Publié le : 1979-06-14
Classification:
Atoms of a partition,
Bernoulli shift,
billiard dynamical system,
$\varepsilon$-independent,
Holder with exponent $\delta$,
"natural" extension,
piecewise $C^2$,
weak-Bernoulli,
weak-mixing,
60F05
@article{1176995050,
author = {Wong, Sherman},
title = {A Central Limit Theorem for Piecewise Monotonic Mappings of the Unit Interval},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 500-514},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995050}
}
Wong, Sherman. A Central Limit Theorem for Piecewise Monotonic Mappings of the Unit Interval. Ann. Probab., Tome 7 (1979) no. 6, pp. 500-514. http://gdmltest.u-ga.fr/item/1176995050/