Building a Stationary Stochastic Process from aFinite - dimensional
Abstract
If A is a nite alphabet, U Z D , and U is a probability measure on A U that \looks like" the marginal projection of a stationary stochas-tic process on A Z D , then can we \extend" U to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some suucient conditions and some necessary conditions for U to be extendible for D > 1, and show that, in general, the problem is not formally decidable.