Geodesic
New results on asymptotic independence of random elements
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 209-236 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we continue the study of asymptotic independence of random elements, which was started in [9]. In the first part we prove some new general facts about asymptotic independence. In the second part we consider the case when the random elements belong to the space of sequences and the case when the joint distributions are Gaussian. 
@article{ZNSL_2020_495_a12,
     author = {S. M. Novikov},
     title = {New results on asymptotic independence of random elements},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {209--236},
     year = {2020},
     volume = {495},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a12/}
}
TY  - JOUR
AU  - S. M. Novikov
TI  - New results on asymptotic independence of random elements
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 209
EP  - 236
VL  - 495
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a12/
LA  - ru
ID  - ZNSL_2020_495_a12
ER  - 
%0 Journal Article
%A S. M. Novikov
%T New results on asymptotic independence of random elements
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 209-236
%V 495
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a12/
%G ru
%F ZNSL_2020_495_a12
S. M. Novikov. New results on asymptotic independence of random elements. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 209-236. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a12/

[1] P. Billingsley, Convergence of probability measures, Wiley Series in Probability and Mathematical Statistics, John Wiley, New York, 1968, xii+253 pp. | MR | Zbl

[2] N. Dunford, J. T. Schwartz, Linear operators, v. 1, General theory, Interscience Publichers, New York–London, 1958, 874 pp. | MR | Zbl

[3] Y. Davydov, V. Rotar', “On asymptotic proximity of distributions”, J. Theor. Probab., 22:1 (2009), 82–98 | DOI | MR | Zbl

[4] R. M. Dudley, Real Analysis and Probability, 2nd edition, Cambridge University Press, 2002, 568 pp. | MR | Zbl

[5] Z. Frolik, “Existence of $l_{\infty}$-partitions of unity”, Rend. Semin. Mat., Torino, 42:1 (1984), 9–14 | MR | Zbl

[6] L. Devroye, A. Mehrabian, T. Reddad, The total variation distance between high-dimensional Gaussians, 2019, arXiv: 1810.08693

[7] A. N. Shiryaev, Veroyatnost, V 2 kn., 3-e izd., pererab. i dop., MTsNMO, M., 2004, 512 pp.

[8] L. Pardo, Statistical Inference Based on Divergence Measures, Statistics: Textbooks and Monographs, 185, Chapman $\$ Hall/CRC, Boca Raton, FL, 2006 | MR | Zbl

[9] Y. Davydov, S. Novikov, Remarks on asymptotic independence, 2019, arXiv: 1910.04243

[10] M. A. Lifshits, Lektsii po gaussovskim protsessam, Uchebnoe posobie, Izdatelstvo ‘Lan’', SPb., 2016, 192 pp.

[11] A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, Berlin–New York, 1995, 402 pp. | MR | Zbl

[12] J. K. Brooks, R. V. Chacon, “Continuity and Compactness of measures”, Adv. in Math., 37:1 (1980), 16–26 | DOI | MR | Zbl