This article is cited in 3 papers

Short Communications

Strengthening of Prokhorov's arcsine-inequality

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The paper proves the strengthening of the known Prokhorov inequality for sums of independent uniformly bounded random variables. An analogous inequality is proved for tails of infinitely divisible distribution functions whose spectral functions are concentrated on some segment.

Keywords: random variable, martingale-difference, filtration, infinitely divisible distribution function, spectral function.

Received: 08.11.2005

DOI: 10.4213/tvp130

 English version: Theory of Probability and its Applications, 2006, 50:4, 677–684

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