Abstract:

The paper gives a characterization of extremal relative stationary probabilities, i.e. extremal probabilities on the set of words of some fixed length whose marginals are invariant w.r.t. all feasible shifts. It is shown that a probability measure is relative stationary if and only if it is the projection of a stationary probability and that each extremal relative stationary probability is the projection of an ergodic probability with a finite support.