Random perturbations of stochastic processes with unbounded variable length memory

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.

PRONEX /FAPESP's[03/09930-9]

Centre National de la Recherche Scientifique - CNRS-FAPESP

CNPq's[475177/2004-5]

CNPq's[308656/2005-9]

Rhythmic patterns, prosodic domains and probabilistic modeling in Portuguese Corpora[485999/2007-2]

FAPESP[06/56980-0]