On some class of functionals on transitions of Markov chain
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 61-82 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The distributions of functionals on transitions of Markov chain are obtained.
Keywords: finite homogeneous Markov chain, functionals for Markov chains.
@article{VNGU_2012_12_2_a6,
     author = {V. S. Lugavov},
     title = {On some class of functionals on transitions of {Markov} chain},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {61--82},
     year = {2012},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a6/}
}
TY  - JOUR
AU  - V. S. Lugavov
TI  - On some class of functionals on transitions of Markov chain
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2012
SP  - 61
EP  - 82
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a6/
LA  - ru
ID  - VNGU_2012_12_2_a6
ER  - 
%0 Journal Article
%A V. S. Lugavov
%T On some class of functionals on transitions of Markov chain
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2012
%P 61-82
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a6/
%G ru
%F VNGU_2012_12_2_a6
V. S. Lugavov. On some class of functionals on transitions of Markov chain. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 61-82. http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a6/

[1] Kolmogorov A. N., “Lokalnaya predelnaya teorema dlya klassicheskikh tsepei Markova”, Izv. AN SSSR. Seriya matem., 13:4 (1949), 281–300 | MR | Zbl

[2] Romanovskii V. I., Diskretnye tsepi Markova, Gostekhizdat, M.–L., 1949

[3] Nagaev S. V., “Nekotorye predelnye teoremy dlya odnorodnykh tsepei Markova”, Teor. ver. i ee primen., 2:4 (1957), 389–416 | MR

[4] Volkov I. S., “O raspredelenii summ sluchainykh velichin, zadannykh na odnorodnoi tsepi Markova s konechnym chislom sostoyanii”, Teor. ver. i ee primen., 3:4 (1958), 413–429 | Zbl

[5] Keilson J., Wishart D. M. G., “A Central Limit Theorem for Processes Defined on a Finite Markov Chain”, Proc. Cambridge Philos. Soc., 60 (1964), 547–567 | DOI | MR | Zbl

[6] Keilson J., Wishart D. M. G., “Addenda to Processes Defined on a Finite Markov Chain”, Proc. Cambridge Philos. Soc., 63 (1967), 187–193 | DOI | MR | Zbl

[7] Chzhun K. L., Odnorodnye tsepi Markova, Mir, M., 1964

[8] Kemeni Dzh. G., Snell Dzh. L., Konechnye tsepi Markova, Nauka, M., 1970

[9] Smirnov N. V., Sarmanov O. V., Zakharov V. K., “Lokalnaya predelnaya teorema dlya chisel perekhodov v tsepi Markova i ee primeneniya”, DAN SSSR, 167:6 (1966), 1238–1241 | MR

[10] Zakharov V. K., Sarmanov O. V., “O zakone raspredeleniya chisla serii v odnorodnoi tsepi Markova”, DAN SSSR, 179:3 (1968), 526–528 | MR

[11] Savelev L. Ya., Balakin S. V., “Sovmestnoe raspredelenie chisla edinits i chisla 1-serii v dvoichnykh markovskikh posledovatelnostyakh”, Diskretnaya matematika, 16:3 (2004), 43–62 | DOI | MR | Zbl

[12] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1986 | MR | Zbl

[13] Lugavov V. S., “On Functionals on the Markov Chain Transitions”, IV International Conference, Novosibirsk, 2006, 22–23

[14] Lugavov V. S., Rogozin B. A., Teoriya vosstanovleniya i faktorizatsionnye tozhdestva dlya bluzhdanii na tsepi Markova, Dep. v VINITI 06.07.88, No 5425-B88

[15] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966 | MR