A family of stationary processes with infinite memory having the same $p$-marginals. Ergodic and spectral properties

Tom 90 / 2001

M. Courbage, D. Hamdan Colloquium Mathematicum 90 (2001), 159-179 MSC: 60Gxx, 28Dxx. DOI: 10.4064/cm90-2-2

Streszczenie

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.

Autorzy

  • M. CourbageL.P.T.M.C.
    Université Paris 7
    2, Place Jussieu
    75251 Paris Cedex 05, France
    e-mail
  • D. HamdanLaboratoire de Probabilités
    4, Place Jussieu
    75252 Paris Cedex 05, France
    e-mail

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