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 how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding ...

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli. Here, we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of ...

Information theory studies how communication systems integrate, encode, compute, and transmit information. The neural system is an example where communication takes place with neurons responding to stimuli and conducting ...

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates ...

The analysis of a stochastic model to describe realistically a practical situation is a hallenge often insurmountable, especially because the real phenomena exhibit dierent dependencies. In this context the Markov models ...