An Application of Skew Product Maps to Markov Chains

Volume 55 / 2007

Zbigniew S. Kowalski Bulletin Polish Acad. Sci. Math. 55 (2007), 35-41 MSC: Primary 37A05; Secondary 60J10. DOI: 10.4064/ba55-1-4


By using the skew product definition of a Markov chain we obtain the following results:

(a) Every $k$-step Markov chain is a quasi-Markovian process.

(b) Every piecewise linear map with a Markovian partition defines a Markov chain for every absolutely continuous invariant measure.

(c) Satisfying the Chapman–Kolmogorov equation is not sufficient for a process to be quasi-Markovian.


  • Zbigniew S. KowalskiInstitute of Mathematics and Informatics
    Wroc/law University of Technology
    Wybrze/ze St. Wyspiańskiego 27
    50-370 Wroc/law, Poland

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