Chains with infinite connections: Uniqueness and Markov representation (Q1087237)

If for a process \((\xi _ n)^{\infty}_{n=-\infty}\) the conditional distribution of \(\xi _ n\) given the past does not depend on n for e.g. \(n\geq 0\), then the process may be called a chain with infinite connections. Under a well-known continuity condition on this conditional distribution the process is shown to be distributed as an instantaneous function of a countable state Markov chain. Also under a certain weaker continuity condition uniqueness of the distributions of the stationary chains is obtained.