Treffer: ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES: On the central and local limit theorem for martingale difference sequences
Title:
ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES: On the central and local limit theorem for martingale difference sequences
Authors:
Contributors:
El Machkouri, Mohamed, Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)
Source:
Stochastics and Dynamics. :153-173
Publication Status:
Preprint
Publisher Information:
World Scientific Pub Co Pte Lt, 2004.
Publication Year:
2004
Subject Terms:
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], local limit theorem, positive entropy, 60F99, 28D05, Probability (math.PR), central limit theorem, Central limit and other weak theorems, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Dynamical systems and their relations with probability theory and stochastic processes, 28D05, measure-preserving transformation, FOS: Mathematics, mixing, martingale difference sequence, 0101 mathematics, 60F99, Mathematics - Probability, rate of convergence
Document Type:
Fachzeitschrift
Article
File Description:
application/pdf; application/xml
Language:
English
ISSN:
1793-6799
0219-4937
0219-4937
DOI:
10.1142/s021949370400105x
DOI:
10.48550/arxiv.math/0403008
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....1d0e2fa2d56ca7e2e7a4ac739351e4b6
Database:
OpenAIRE
Weitere Informationen
Let [Formula: see text] be a Lebesgue space and T: Ω→Ω an ergodic measure-preserving automorphism with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on Ω with a common nondegenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.