Geodesic
Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 16-39
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper obtains upper and low estimates of the metric $\varepsilon$-entropy of the arithmetic averages for classes of stationary sequences coinciding in the order of growth as $\varepsilon\to 0$. These estimates essentially differ from the estimates for analogous classes of quasi-stationary processes.
Keywords: stationary and quasi-stationary sequences, arithmetic averages, metric entropy, upper and low estimates. 
@article{TVP_2008_53_1_a1,
     author = {V. F. Gaposhkin},
     title = {Exact {Estimates} of the {Metric} {Entropy} of the {Averages} for {Some} {Classes} of {Stationary} {Sequences}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {16--39},
     year = {2008},
     volume = {53},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a1/}
}
TY  - JOUR
AU  - V. F. Gaposhkin
TI  - Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2008
SP  - 16
EP  - 39
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a1/
LA  - ru
ID  - TVP_2008_53_1_a1
ER  - 
%0 Journal Article
%A V. F. Gaposhkin
%T Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2008
%P 16-39
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a1/
%G ru
%F TVP_2008_53_1_a1
V. F. Gaposhkin. Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 16-39. http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a1/

[1] Talagrand M., “Applying a theorem of Fernique”, Ann. Inst. H. Poincaré, 32:6 (1996), 779–799 | MR | Zbl

[2] Weber M., Entropie métrique et convergence presque partout, Hermann, Paris, 1998, 151 pp. | MR | Zbl

[3] Gamet C., Weber M., “Entropy numbers of some ergodic averages”, Teoriya veroyatn. i ee primen., 44:4 (1999), 776–795 | MR | Zbl

[4] Gaposhkin V. F., “Otsenki entropii mnozhestva srednikh nekotorykh klassov statsionarnykh i kvazistatsionarnykh posledovatelnostei”, Matem. zametki, 78:1 (2005), 52–58 | MR | Zbl

[5] Gaposhkin V. F., “Tochnye otsenki metricheskoi entropii mnozhestva srednikh kvazistatsionarnykh protsessov”, Teoriya veroyatn. i ee primen., 51:4 (2006), 785–793 | MR

[6] Zigmund A., Trigonometricheskie ryady, v. I, IL, M., 1965, 615 pp. | MR

[7] Gaposhkin V. F., “Otsenki srednikh dlya pochti vsekh realizatsii statsionarnykh protsessov”, Sib. matem. zhurn., 20:5 (1979), 978–989 | MR | Zbl

[8] Kachurovskii A. G., “Skorosti skhodimosti v ergodicheskikh teoremakh”, Uspekhi matem. nauk, 51:4 (1996), 73–124 | MR

[9] Gaposhkin V. F., “O skorosti ubyvaniya veroyatnostei $\varepsilon$-uklonenii srednikh statsionarnykh protsessov”, Matem. zametki, 64:3 (1998), 366–372 | MR | Zbl