Markov Chains with Positive Transitions Are Not Determined by Anyp-Marginals

An ergodic Markov chain is not determine

An ergodic Markov chain is not determined by its two-dimensional marginal laws

✍ M. Courbage; D. Hamdan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 326 KB

For any ergodic Markov chain (X,) on a finite state space K, we construct a class of ergodic stationary processes on K having the same two-dimensional marginal laws as (At,) but with distinct laws. The same construction also allows us to exhibit projections of some ergodic Markov chains that are not