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Teoriya Veroyatnostei i ee Primeneniya, 1973, Volume 18, Issue 3, Pages 593–595
(Mi tvp2731)
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This article is cited in 1 scientific paper (total in 1 paper)
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 $\int_{|x|\ge\delta}\frac{|x|^\alpha\,dF(x)}{\psi(x)}$.
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
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https://www.mathnet.ru/eng/tvp2731 https://www.mathnet.ru/eng/tvp/v18/i3/p593
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Abstract page: | 165 | Full-text PDF : | 75 |
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