Geodesic
On convergence rates for homogeneous Markov chains
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 16-19.

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

New improved rates of convergence for ergodic homogeneous Markov chains are studied. Examples of comparison with classical rate bounds are provided.
Keywords: Markov chains, ergodicity, convergence rate. 
@article{DANMA_2020_490_a3,
     author = {A. Yu. Veretennikov and M. A. Veretennikova},
     title = {On convergence rates for homogeneous {Markov} chains},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {16--19},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a3/}
}
TY  - JOUR
AU  - A. Yu. Veretennikov
AU  - M. A. Veretennikova
TI  - On convergence rates for homogeneous Markov chains
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 16
EP  - 19
VL  - 490
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_490_a3/
LA  - ru
ID  - DANMA_2020_490_a3
ER  - 
%0 Journal Article
%A A. Yu. Veretennikov
%A M. A. Veretennikova
%T On convergence rates for homogeneous Markov chains
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 16-19
%V 490
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_490_a3/
%G ru
%F DANMA_2020_490_a3
A. Yu. Veretennikov; M. A. Veretennikova. On convergence rates for homogeneous Markov chains. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 16-19. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a3/

[1] Seneta E., Non-negative Matrices and Markov Chains, Springer, N.Y., 1981 | DOI | MR | Zbl

[2] Veretennikov A.Yu., “Ergodic Markov processes and Poisson equations (lecture notes)”, Modern problems of stochastic analysis and statistics, Selected contributions in honor of Valentin Konakov, ed. V. Panov, Springer, 2017, 457–511 | DOI | MR | Zbl

[3] Gantmakher F.R., Teoriya matrits, 5-e izd., Fizmatlit, M., 2004 | MR

[4] Butkovsky O.A., Veretennikov A.Yu., “On Asymptotics for Vaserstein Coupling of Markov Chains”, Stochastic Processes and Their Applications, 123:9 (2013), 3518–3541 | DOI | MR | Zbl

[5] Lindvall T., Lectures on the Coupling Method, Dover, 2002 | MR | Zbl

[6] Vasershtein L.N., “Markovskie protsessy na schetnom proizvedenii prostranstv, opisyvayuschie bolshie sistemy avtomatov”, Probl. peredachi inform., 5:3 (1969), 64–72 | MR

[7] Dynkin E.B., Markovskie protsessy, Fizmatgiz, M., 1963

[8] Markov A.A., “Rasprostranenie zakona bolshikh chisel na velichiny, zavisyaschie drug ot druga”, Izv. fiz.-matem., Kazan. univ., 15 (1906), 135–156

[9] Dobrushin R.L., “Tsentralnaya predelnaya teorema dlya neodnorodnykh tsepei Markova I, II”, Teoriya veroyatn. i ee primeneniya, 1956, no. 1, 72–89 ; No 4, 365–425 | MR | Zbl

[10] Kalashnikov V.V., “Metod skleivaniya, ego razvitie i primeneniya”: E. Nummelin, Obschie neprivodimye tsepi Markova i neotritsatelnye operatory, Mir, M., 1989, 176–190

[11] Krasnoselskii M.A., Lifshits E.A., Sobolev A.V., Pozitivnye lineinye sistemy. Metod polozhitelnykh operatorov, Teoriya i metody sistemnogo analiza, Nauka, M., 1985

[12] Nummelin E., General Irreducible Markov Chains, CUP, Cambridge, 2008 | DOI