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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 4, Pages 729–734
(Mi tvp759)
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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
Some generalizations of limit theorems of theory of probability
Yu. P. Studnev Uzhgorod
Abstract:
Let $\xi_1,\dots,\xi_n,\dots$ be a sequence of independent random variables with non-monotonic distribution functions $V_1(x),\dots,V_n(x),\dots$ belonging to the class $В$ (i.e. $V_i(x)$ satisfy the condition (1.3)). The paper contains some results on convergence of distribution functions of sums
$$
s_n=\frac{\xi_1+\dots+\xi_n}{B_n}
$$
In to the functions $\Phi_{2q}(x)$ having “densities”
$$
\varphi_{2q}(x)=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-itx-\frac{t^{2q}}{(2q)}}\,dt.
$$
Received: 22.03.1965
Citation:
Yu. P. Studnev, “Some generalizations of limit theorems of theory of probability”, Teor. Veroyatnost. i Primenen., 12:4 (1967), 729–734; Theory Probab. Appl., 12:4 (1967), 668–672
Linking options:
https://www.mathnet.ru/eng/tvp759 https://www.mathnet.ru/eng/tvp/v12/i4/p729
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