The paper continues the study of asymptotic independence of random elements, which was started by the author and Y. Davydov (2019). In the first part, some new general facts about asymptotic independence are proved. In the second part, the case when the random elements belong to the space of sequences and the case when the joint distributions are Gaussian is considered.
Similar content being viewed by others
References
P. Billingsley, Convergence of Probability Measures, John Wiley, New York (1968).
N. Dunford and J. T. Schwartz, Linear Operators, Interscience Publichers, Ney York, London (1958).
Y. Davydov and V. Rotar’, “On asymptotic proximity of distributions,” J. Theor. Probab. 22, No. 1, 82–98 (2009).
R. M. Dudley, Real Analysis and Probability, 2nd edition, Cambridge University Press (2002).
Z. Frolik, “Existence of l∞-partitions of unity,” Rend. Semin. Mat., Torino, 42, No. 1, 9–14 (1984).
L. Devroye, A. Mehrabian, and T. Reddad, The total variation distance between highdimensional Gaussians, https://arxiv.org/abs/1810.08693 (2019).
A. N. Shiryaev, Probability, 3rd edition, Moscow (2004).
L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall/CRC, Boca Raton (2006).
Y. Davydov and S. Novikov, Remarks on asymptotic independence, https://arxiv.org/abs/1910.04243 (2019).
M. A. Lifshits, Lectures on Gaussian Processes, Lan’, St.Petersburg (2016).
A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag Berlin, New York (1995).
J. K. Brooks and R. V. Chacon, “Continuity and Compactness of measures,” Adv. Math., 37, No. 1, 16–26 (1980).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 209–236.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Novikov, S.M. New Results on Asymptotic Independence of Random Elements. J Math Sci 268, 663–683 (2022). https://doi.org/10.1007/s10958-022-06237-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-022-06237-5