Martingales and first passage times of AR(1) sequences
Probability
2008-01-03 v1
Abstract
Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.
Keywords
Cite
@article{arxiv.0712.3468,
title = {Martingales and first passage times of AR(1) sequences},
author = {Alexander Novikov and Nino Kordzakhia},
journal= {arXiv preprint arXiv:0712.3468},
year = {2008}
}
Comments
To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)