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 Mat. Zametki, 1972, Volume 12, Issue 3, Pages 295–302 (Mi mz9882)

The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states

D. V. Senchenko

M. V. Lomonosov Moscow State University

Abstract: It is proved that the final $\sigma$-algebra in the case of an inhomogeneous Markov chain with a finite number of states $n$ is generated by a finite number ($\leqslant n$) of atoms. The atoms are characterized from the point of view of the behavior of trajectories of the chain. Sufficient conditions are given (in the case of a countable number of states) that there should exist an unique atom at infinity.

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English version:
Mathematical Notes, 1972, 12:3, 610–613

Bibliographic databases:

UDC: 519.2

Citation: D. V. Senchenko, “The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states”, Mat. Zametki, 12:3 (1972), 295–302; Math. Notes, 12:3 (1972), 610–613

Citation in format AMSBIB
\Bibitem{Sen72} \by D.~V.~Senchenko \paper The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states \jour Mat. Zametki \yr 1972 \vol 12 \issue 3 \pages 295--302 \mathnet{http://mi.mathnet.ru/mz9882} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=321187} \zmath{https://zbmath.org/?q=an:0267.60071} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 3 \pages 610--613 \crossref{https://doi.org/10.1007/BF01093996}