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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 3, Pages 593–595 (Mi tvp2731)  

Short Communications

On the moments of distributions attracted to stable laws

V. V. Petrov

Leningrad

Abstract: The following theorem is proved. Let the distribution function $F(x)$ belong to the domain of the normal attraction of a stable law with exponent $\alpha$, $0<\alpha<2$. If $\delta>0$ and $\psi(x)$ is an even function which is positive and nondecreasing on the half-line $x\ge\delta$, then convergence of the integral $\int_\delta^\infty\frac{dx}{x\psi(x)}$ is equivalent to convergence of the integral $\int_{|x|\ge\delta}\frac{|x|^\alpha dF(x)}{\psi(x)}$.

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English version:
Theory of Probability and its Applications, 1974, 18:3, 569–571

Bibliographic databases:

Received: 24.01.1972

Citation: V. V. Petrov, “On the moments of distributions attracted to stable laws”, Teor. Veroyatnost. i Primenen., 18:3 (1973), 593–595; Theory Probab. Appl., 18:3 (1974), 569–571

Citation in format AMSBIB
\Bibitem{Pet73}
\by V.~V.~Petrov
\paper On the moments of distributions attracted to stable laws
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 3
\pages 593--595
\mathnet{http://mi.mathnet.ru/tvp2731}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=326802}
\zmath{https://zbmath.org/?q=an:0323.60027}
\transl
\jour Theory Probab. Appl.
\yr 1974
\vol 18
\issue 3
\pages 569--571
\crossref{https://doi.org/10.1137/1118070}


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