This article is cited 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

 English version: Theory of Probability and its Applications, 1967, 12:4, 668–672

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