Random perturbations of stochastic chains with unbounded variable length memory
Probability
2007-07-20 v1
Abstract
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.
Cite
@article{arxiv.0707.2796,
title = {Random perturbations of stochastic chains with unbounded variable length memory},
author = {Pierre Collet and Antonio Galves and Florencia G. Leonardi},
journal= {arXiv preprint arXiv:0707.2796},
year = {2007}
}