An ergodic Markov chain is not determined by its two-dimensional marginal laws. (English) Zbl 0928.60052
Summary: For any ergodic Markov chain \((X_n)\) on a finite state space \(K\), we construct a class of ergodic stationary processes on \(K\) having the same two-dimensional marginal laws as \((X_n)\) but with distinct laws. The same construction also allows us to exhibit projections of some ergodic Markov chains that are not determined by their two-dimensional marginal laws.
MSC:
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
References:
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