Geodesic
Identification of a~binary Markov chain of order~$s$ with~$r$ partial connections subjected to additive distortions
Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 138-155.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the solution of an actual problem of identification (estimation of parameters and hypotheses testing) for the so-called binary Markov chain of order $s$ with $r$ partial connections $\mathcal{MC}(s,r)$ subjected to additive distortions. 
@article{DM_2010_22_4_a9,
     author = {Yu. S. Kharin and A. I. Petlitskii},
     title = {Identification of a~binary {Markov} chain of order~$s$ with~$r$ partial connections subjected to additive distortions},
     journal = {Diskretnaya Matematika},
     pages = {138--155},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_4_a9/}
}
TY  - JOUR
AU  - Yu. S. Kharin
AU  - A. I. Petlitskii
TI  - Identification of a~binary Markov chain of order~$s$ with~$r$ partial connections subjected to additive distortions
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 138
EP  - 155
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_4_a9/
LA  - ru
ID  - DM_2010_22_4_a9
ER  - 
%0 Journal Article
%A Yu. S. Kharin
%A A. I. Petlitskii
%T Identification of a~binary Markov chain of order~$s$ with~$r$ partial connections subjected to additive distortions
%J Diskretnaya Matematika
%D 2010
%P 138-155
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2010_22_4_a9/
%G ru
%F DM_2010_22_4_a9
Yu. S. Kharin; A. I. Petlitskii. Identification of a~binary Markov chain of order~$s$ with~$r$ partial connections subjected to additive distortions. Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 138-155. http://geodesic.mathdoc.fr/item/DM_2010_22_4_a9/

[1] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Osnovy kriptografii, Gelios, Moskva, 2001

[2] Dub Dzh., Veroyatnostnye protsessy, IL, Moskva, 1956

[3] Zubkov A. M., “Datchiki psevdosluchainykh chisel i ikh primeneniya”, Trudy II Mezhdunarodnoi nauchnoi konf. “Matematika i bezopasnost informatsionnykh tekhnologii”, Izd-vo MGU, Moskva, 2003, 200–206 | MR

[4] Kharin Yu. S., Bernik V. I, Matveev G. V., Agievich S. V., Matematicheskie i kompyuternye osnovy kriptologii, Novoe znanie, Minsk, 2003

[5] Maksimov Yu. I., “O tsepyakh Markova, svyazannykh s dvoichnymi registrami sdviga so sluchainymi elementami”, Trudy po diskretnoi matematike, 1, 1997, 203–220 | MR | Zbl

[6] Jacobs P. A., Lewis P. A. W., “Discrete time series generated by mixtures. I: Correlational and runs properties”, J. Royal Stat. Soc. Ser. B, 40 (1978), 94–105 | MR | Zbl

[7] Raftery A. E., “A model for high-order Markov chains”, J. Royal Statist. Soc., 47 (1985), 528–539 | MR | Zbl

[8] Bühlmann P., Wyner A., “Variable length Markov chains”, Ann. Stat., 27:2 (1999), 480–513 | DOI | MR | Zbl

[9] Kharin Yu. S., “Tsepi Markova s $r$-chastichnymi svyazyami i ikh statisticheskoe otsenivanie”, Dokl. NAN Belarusi, 48:1 (2004), 40–44 | MR | Zbl

[10] Kharin Yu. S., Petlitskii A. I., “Tsep Markova $s$-go poryadka s $r$ chastichnymi svyazyami i statisticheskie vyvody o ee parametrakh”, Diskretnaya matematika, 19:2 (2007), 109–130 | MR | Zbl

[11] Sugimoto S., Ishizuka I., “Identification and estimation algorithms for a Markov chain plus AR process”, Proc. IEEE ICASSP, 8 (1983), 247–250

[12] Rabiner L. R., “A tutorial on hidden Markov models and selected applications in speech recognition”, Proc. IEEE, 77 (1989), 257–286 | DOI

[13] Berchtold A., “The double chain Markov model”, Commun. Stat. Theory Methods, 28:11 (1999), 2569–2589 | DOI | MR | Zbl

[14] Kemeni Dzh. G., Snell Dzh. L., Konechnye tsepi Markova, Nauka, Moskva, 1970

[15] Kharin Yu. S., Petlitskii A. I., “Ob otsenivanii poryadka tsepi Markova s chastichnymi svyazyami”, Trudy IST, 1, 2006, 156–161

[16] Csiszar I., Shields P. C., “The consistency of the BIC Markov order estimator”, Ann. Stat., 28:6 (2000), 1601–1619 | DOI | MR | Zbl

[17] Petlitskii A. I., Kharin Yu. S., “Statisticheskii analiz dvoichnoi tsepi Markova s chastichnymi svyazyami pri nalichii additivnykh iskazhenii”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2008, no. 4, 30–36 | MR

[18] Shiryaev A. N., Veroyatnost, Nauka, Moskva, 1989 | MR

[19] Bradley R. C., “Basic properties of strong mixing conditions. A survey and some open questions”, Probab. Surv., 2 (2005), 107–144 | DOI | MR | Zbl

[20] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, Moskva, 1965

[21] Borovkov A. A., Matematicheskaya statistika, Nauka, Moskva, 1984 | MR | Zbl

[22] Gantmakher F. R., Teoriya matrits, Nauka, Moskva, 1966 | MR

[23] Ivchenko G. I., Medvedev Yu. I., Matematicheskaya statistika, Vysshaya shkola, Moskva, 1984 | MR | Zbl

[24] Bolshev L. N., Smirnov N. V., Tablitsy matematicheskoi statistiki, Nauka, Moskva, 1983 | MR

[25] Samarskii A. A., Gulin A. V., Chislennye metody, Nauka, Moskva, 1989 | MR

[26] Gourieroux C., Monfort A., Statistics and econometric models: General concepts, estimation, prediction, and algorithms, v. 1, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl