Geodesic
A family of stationary processes with infinite memory having the same $p$-marginals. Ergodic and spectral properties
M. Courbage 1   ; D. Hamdan 2
1 L.P.T.M.C. Université Paris 7 2, Place Jussieu 75251 Paris Cedex 05, France
2 Laboratoire de Probabilités 4, Place Jussieu 75252 Paris Cedex 05, France
Colloquium Mathematicum, Tome 90 (2001) no. 2, pp. 159-179 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We construct a large family of ergodic non-Markovian processes with infinite memory having the same $p$-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman–Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.
DOI : 10.4064/cm90-2-2
Keywords: construct large family ergodic non markovian processes infinite memory having p dimensional marginal laws arbitrary ergodic markov chain projection markov chains their spectral mixing properties given chapman kolmogorov equation ergodic transition matrix generically satisfied infinite memory processes

M. Courbage  1   ; D. Hamdan  2

1 L.P.T.M.C. Université Paris 7 2, Place Jussieu 75251 Paris Cedex 05, France
2 Laboratoire de Probabilités 4, Place Jussieu 75252 Paris Cedex 05, France 
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Ergodic and spectral properties
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Ergodic and spectral properties
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M. Courbage; D. Hamdan. A family of stationary processes with infinite
memory having the same $p$-marginals.
Ergodic and spectral properties. Colloquium Mathematicum, Tome 90 (2001) no. 2, pp. 159-179. doi: 10.4064/cm90-2-2

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