An application of skew product maps to Markov chains

• Autorzy: Kowalski Z. S.
• Języki publikacji: EN

Abstrakty

EN

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 forevery absolutely continuous invariant measure. (c) Satisfying the Chapman-Kolmogorov equation is not sufficient for a process to be quasi-Markovian.

Słowa kluczowe

EN

skew product; Markov chain; quasi-Markovian process

PL

proces Markowa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 1
• Strony: 35--41
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kowalski Z. S.

• Institute of Mathematics and Informatics, Wroclaw University of Technology, Wybrzeże St. Wyspiańskiego 27, 50-370 Wroclaw, Poland,

Bibliografia

• [1] J. Aaronson and M. Denker, Local limit theorems for Gibbs-Markov maps, Stoch. Dyn. 1 (2001), 193-237.
• [2] J. Aaronson, M. Denker, O. Sarig and R. Zweimiiller, Aperiodicity of cocycles and conditional local limit theorems, ibid. 4 (2004), 31-62.
• [3] M. Courbage and D. Hamdan, An ergodic Markov chain is not determined by its two-dimensional marginal laws, Statist. Probab. Lett. 37 (1998), 35-40.
• [4] Z. S. Kowalski, Quasi-Markovian transformations, Ergodic Theory Dynam. Systems 17 (1997), 885-897.
• [5] T. Morita, Deterministic version lemmas in ergodic theory of random dynamical systems, Hiroshima Math. J. 18 (1988), 15-29.
• [6] W. Parry, Entropy and Generators in Ergodic Theory, Benjamin, New York, 1969.
• [7] I. Shiokawa, Ergodic properties of piecewise linear transformations, Proc. Japan Acad. 46 (1970), 1122-1125.
• [8] K. M. Wilkinson, Ergodic properties of a class of piecewise linear transformations, Z. Wahrsch. Verw. Gebiete 31 (1975), 303-328.