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Theory of Probability and Mathematical Statistics



Estimation of the convergence velocity in the central limit theorem for a sequence of series in terms of mean pseudo-moments

M. M. Kapustey, P. V. Slyusarchuk

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Abstract: Article contains generalization of the Zolotarev V. M. estimates for a sequence of series of differently distributed random variable in terms of average pseudomoments. Method of Zolotarev is used in proof.

Keywords: Convergence, central limit theorem, pseudomoments, sequence of series, different (non-identical) distributed random variables.

Bibliography:
1. V. M. Zolotarev, On the closeness the distribution of two sum of independent random variables, Teor. Verojatn., 10 (1965), 519-526.
2. V. Paulauskas, One intensification of the Lyapunov theorem, Lituan. Math. J., 9 (1969), 323-328.
3. V. M. Zolotarev, Exactness of an approximation in the central limit theorem , Proceedings of the Second Japan‒USSR Symposium on Probability Theory, Lecture Notes in Mathematics, vol. 330, Springer-Verlag, Berlin, 1973, p. 531-543.
4. V. M. Zolotarev, Modern theory of summation of independent random variables, Nauka, Moscow, 1986.
5. Yu. Mishura, Ye. Munchak, P. Slyusarchuk, The rate of convergence to the normal law in therms of psevdomoments, Modern Stochastics: Theory and Applications, 2 (2015), no. 2, 95-106.
6. Yu. Mishura, Ye. Munchak, The convergence rate of stock prices using the method of pseudo-moments, Teor. Imovir. ta Matem. Statyst., 92 (2015), 110-124.
7. P. V. Slyusarchuk, I. Y. Polyak, The generalization of one result of V. M. Zolotarev , Nauk. vistn. Uzhorod. Univer. Seriya matem., 3 (1998), 184-189.
8. T. V. Bojarishcheva, P. V. Slyusarchuk, The estimate of the rate of convergence in the central limit theorem for differently distributed variables, Nauk. vistn. Uzhorod. Univer. Seriya matem., 4 (1999), 12-16.
9. M. M. Loeve, Probability Theory, Izd. Inostr. Lit., Moscow, 1962.