Geodesic
The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states
Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 295-302 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_1972_12_3_a10,
     author = {D. V. Senchenko},
     title = {The final $\sigma$-algebra of an inhomogeneous {Markov} chain with a finite number of states},
     journal = {Matemati\v{c}eskie zametki},
     pages = {295--302},
     year = {1972},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a10/}
}
TY  - JOUR
AU  - D. V. Senchenko
TI  - The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states
JO  - Matematičeskie zametki
PY  - 1972
SP  - 295
EP  - 302
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a10/
LA  - ru
ID  - MZM_1972_12_3_a10
ER  - 
%0 Journal Article
%A D. V. Senchenko
%T The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states
%J Matematičeskie zametki
%D 1972
%P 295-302
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a10/
%G ru
%F MZM_1972_12_3_a10
D. V. Senchenko. The final $\sigma$-algebra of an inhomogeneous Markov chain with a finite number of states. Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 295-302. http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a10/