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 …

Stochastic chains with memory of variable length constitute an interesting family of
stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a …

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of
a version of the algorithm Context, when the underlying tree is not necessarily bounded. The …

We observe a length-n sample generated by an unknown, stationary ergodic Markov
process (model) over a finite alphabet A. Given any string w of symbols from A we want …

Abstract We present the Probabilistic Context Neighborhood model designed for two-
dimensional lattices as a variation of a Markov random field assuming discrete values. In this …

We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of
unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also …

We derive explicit upper bounds for the d-distance between a chain of in nite order and its
canonical k-steps Markov approximation. Our proof is entirely construc-tive and involves …

Stationary ergodic processes with finite alphabets are approximated by finite memory
processes based on an n-length realization of the process. Under the assumptions of …

These lecture notes present new results on statistical model selection for stochastic systems.
The majority of the results are original and first appeared in several recent papers co …

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 …