Building a Stationary Stochastic Process From a Finite-Dimensional Marginal
Marcus Pivato · Canadian Journal of Mathematics · 2001
Abstract If is a finite alphabet, , and is a probability measure on that “looks like” the marginal projection of a stationary stochastic process on , then can we “extend” 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 sufficient conditions and some necessary conditions for to be extendible for D > 1, and show that, in general, the problem is not formally decidable.