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Examples of ergodic processes uniquely determined by their two-marginal laws

✍ Scribed by M. Courbage; D. Hamdan

Book ID: 104301565
Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 97 KB
Volume: 52
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(00)00190-5

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✦ Synopsis

We show that the stationary processes associated to some two-cell partitions induced by the irrational rotation of the circle and by Kronecker Gaussian processes are uniquely determined by their two-dimensional marginals.

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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