Geodesic
Nonnegative chainable matrices and Kolmogorov's condition
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 5-20 
Yu. A. Al'pin; I. V. Bashkin. Nonnegative chainable matrices and Kolmogorov's condition. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 5-20. http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a0/
@article{ZNSL_2021_504_a0,
     author = {Yu. A. Al'pin and I. V. Bashkin},
     title = {Nonnegative chainable matrices and {Kolmogorov's} condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--20},
     year = {2021},
     volume = {504},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a0/}
}
TY  - JOUR
AU  - Yu. A. Al'pin
AU  - I. V. Bashkin
TI  - Nonnegative chainable matrices and Kolmogorov's condition
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 5
EP  - 20
VL  - 504
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a0/
LA  - ru
ID  - ZNSL_2021_504_a0
ER  - 
%0 Journal Article
%A Yu. A. Al'pin
%A I. V. Bashkin
%T Nonnegative chainable matrices and Kolmogorov's condition
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 5-20
%V 504
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a0/
%G ru
%F ZNSL_2021_504_a0

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper proves that an indecomposable nonnegative matrix is chainable if and only if it satisfies Kolmogorov's condition, under which the Markov chain determined by a stochastic matrix obeys the multidimensional local limit theorem.

[1] Yu. A. Alpin, I. V. Bashkin, “Neotritsatelnye tsepnye matritsy”, Zap. nauchn. semin. POMI, 496, 2020, 5–25

[2] Yu. A. Alpin, Neotritsatelnye matritsy, Kazan. fed. un-t, 2015

[3] R. Sinkhorn, P. Knopp, “Problems involving diagonal products in nonnegative matrices”, Trans. Amer. Math. Soc., 136 (1969), 67–75 | DOI | MR | Zbl

[4] J. Hartfiel, J. Maxson, “The chainable matrix, a special combinatorial matrix”, Discrete Math., 12 (1975), 245–256 | DOI | MR | Zbl

[5] T. A. Sarymsakov, “O neodnorodnykh tsepyakh Markova”, Dokl. AN SSSR, 120 (1958), 465–467 | Zbl

[6] A. N. Kolmogorov, “Lokalnaya predelnaya teorema dlya klassicheskikh tsepei Markova”, Izv. AN SSSR. Ser. matem., 13 (1949), 281–300 | Zbl

[7] I. Z. Rozenknop, “O nekotorykh svoistvakh sovokupnosti zamknutykh putei v sisteme iz n sostoyanii s zadannymi perekhodami mezhdu nimi”, Izv. AN SSSR. Ser. matem., 14 (1950), 95–100 | MR | Zbl

[8] Yu. A. Alpin, I. V. Bashkin, “Neotritsatelnye tsepnye matritsy i uslovie Kolmogorova”, Sb. trudov Mezhd. konf. po algebre, analizu i geometrii, Kazan. fed. un-t, 2021