  This paper introduces the concept of random context representations for the
transition probabilities of a finite-alphabet stochastic process. Processes
with these representations generalize context tree processes (a.k.a. variable
length Markov chains), and are proven to coincide with processes whose
transition probabilities are almost surely continuous functions of the
(infinite) past. This is similar to a classical result by Kalikow about
continuous transition probabilities. Existence and uniqueness of a minimal
random context representation are proven, and an estimator of the transition
probabilities based on this representation is shown to have very good "pastwise
adaptativity" properties. In particular, it achieves minimax performance, up to
logarithmic factors, for binary renewal processes with bounded $2+\gamma$
moments.
