Abstract
An estimate of the rate of strong convergence of convolutions of probability measures is given under the assumption that the components of each convolution converge weakly and in total variation, respectively.
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K. R. Parthasarathy and T. Steerneman, “A tool in establishing total variation convergence,”Proc. Am. Math. Soc.,95, 626–630 (1985).
Yu. Davydov, “On strong convergence for distributions of functionals of stochastic processes, I, II,”Teor. Veroyatn. Primen.,25, 782–799 (1980);26, 266–286 (1981).
Yu. Davydov, “Note on a theorem of Parthasarathy-Steerneman,”J. Sci. Technol. Chengdu Univ.,5, 75–80 (1990).
V. N. Sudakov,Geometrical Problems in the Theory of Infinite-Dimensional Probability Distributions [in Russian], Nauka, Leningrad (1976).
S. Rachev,Probability Metrics and the Stability of Stochastic Models, Wiley, New York (1991).
A. V. Kakosyan and L. B. Klebanov, “On estimates of the closeness of distributions in terms of characteristic functions,”Teor. Veroyatn. Primen.,29, 815–816 (1984).
S. Bochner,Harmonic Analysis and the Theory of Probability, California Univ. Press, Berkeley and Los Angeles (1960).
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Reported at the XVI Seminar on Stability Problems for Stochastic Models, Eger, Hungary, 29 August–3 September 1994. Received by the Editorial Board 15 January, 1996.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II.
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Davydov, Y. On the rate of strong convergence for convolutions. J Math Sci 83, 393–396 (1997). https://doi.org/10.1007/BF02400923
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DOI: https://doi.org/10.1007/BF02400923