Building a Stationary Stochastic Process From a Finite-dimensional Marginal
Probability
2007-05-23 v1 Dynamical Systems
Abstract
If A is a finite alphabet, Z^D is a D-dimensional lattice, U is a subset of Z^D, and mu_U is a probability measure on A^U that ``looks like'' the marginal projection of a stationary random field on A^(Z^D), then can we ``extend'' mu_U to such a field? 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 mu_U to be extendible for D > 1, and show that, in general, the problem is not formally decidable.
Keywords
Cite
@article{arxiv.math/0108081,
title = {Building a Stationary Stochastic Process From a Finite-dimensional Marginal},
author = {Marcus Pivato},
journal= {arXiv preprint arXiv:math/0108081},
year = {2007}
}
Comments
LaTeX2E format, 40 pages, 4 figures (eps format)