Weakly dependent chains with infinite memory
Probability
2007-12-20 v1 Statistics Theory
Statistics Theory
Abstract
We prove the existence of a weakly dependent strictly stationary solution of the equation called {\em chain with infinite memory}. Here the {\em innovations} constitute an independent and identically distributed sequence of random variables. The function takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments and the rate of decay of the Lipschitz coefficients of the function . With the help of the weak dependence properties, we derive Strong Laws of Large Number, a Central Limit Theorem and a Strong Invariance Principle.
Keywords
Cite
@article{arxiv.0712.3231,
title = {Weakly dependent chains with infinite memory},
author = {Paul Doukhan and Olivier Wintenberger},
journal= {arXiv preprint arXiv:0712.3231},
year = {2007}
}
Comments
Stochastic Processes and their Applications (2008) accept\'e