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Teoriya Veroyatnostei i ee Primeneniya, 1973, Volume 18, Issue 2, Pages 350–357
(Mi tvp4293)
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This article is cited in 15 scientific papers (total in 15 papers)
Absolute Estimates for Moments of Certain Boundary Functionals
A. A. Mogul'skii Novosibirsk
Abstract:
Let $\xi_1,\xi_2,\dots$ be independent identically distributed random variables, $\mathbf{M}\xi_1\ge 0$, and let $\chi$ is the limiting value of the first jump over an infinite bound. In the paper, the estimates
$$
\mathbf{M}\chi^s\le A_1\frac{1}{s+1}\frac{\mathbf{M}|\xi_1|^{s+2}}{\mathbf{M}\xi^2_1},\qquad s\ge 0,
$$
are obtained.
Received: 27.10.1970 Revised: 10.05.1972
Citation:
A. A. Mogul'skii, “Absolute Estimates for Moments of Certain Boundary Functionals”, Teor. Veroyatnost. i Primenen., 18:2 (1973), 350–357; Theory Probab. Appl., 18:2 (1973), 340–347
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https://www.mathnet.ru/eng/tvp4293 https://www.mathnet.ru/eng/tvp/v18/i2/p350
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