Literature cited
V. M. Zolotarev, “Metric distances in spaces of random variables and their distributions,” Mat. Sb.,101, No. 3, 416–454 (1976).
V. V. Yurinskii, “On the accuracy of the normal approximation to the probability of hitting a ball,” Teor. Veroyatn. Primen.,27, No. 2, 270–278 (1982).
S. V. Nagaev, “On accuracy of normal approximation for distribution of sum of independent Hilbert space valued random variables,” in: Fourth Soviet-Japanese Symposium on Probability Theory and Mathematical Statistics, Abstracts of Papers, Metsniereba, Tbilisi, Vol. 2, pp. 131–132.
Yu. V. Borovskikh and A. Rachkauskas, “Asymptotic behavior of distributions in Banach spaces,” Litov. Mat. Sb.,19, No. 4, 39–54 (1979).
A. Rachkauskas, “On convergence in uniform metric of sums of independent random variables with values in a Hilbert space,” Litov. Mat. Sb.,21, No. 3, 90–98 (1981).
L. V. Osipov and V. I. Rotar', “On rate of convergence in many-dimensional and infinitely dimensional central limit theorems,” in: Third International Vil'nyus Conference on Probability Theory and Mathematical Statistics, Abstracts of Papers [in Russian], Vol. 2, Inst. Mat. Kibern., Akad. Nauk LitSSR, Vilnius (1981), pp. 97–98.
S. V. Nagaev and V. I. Chebotarev, “On rate of convergence bounds in the central limit theorem for random variables with values in the space Z2,” In: Mathematical Analysis and Related Topics [in Russian], Nauka, Novosibirsk (1978), pp. 153–182.
V. V. Senatov, “Some uniform bounds on rate of convergence in multidimensional central limit theorem,” Teor. Veroyatn. Primen.,25, 757–770 (1980).
Additional information
Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei — Trudy Seminara, pp. 128–135, 1984.
In conclusion, I would like to thank V. M. Zolotarev for constant attention to this study.
Rights and permissions
About this article
Cite this article
Senatov, V.V. Orders of rate of convergence bounds in a Hilbert-space central limit theorem. J Math Sci 35, 2394–2401 (1986). https://doi.org/10.1007/BF01105658
Issue Date:
DOI: https://doi.org/10.1007/BF01105658