This article is cited in 18 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

 English version: Theory of Probability and its Applications, 1973, 18:2, 340–347

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