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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

CiteScore 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.177
Source Normalized Impact per Paper (SNIP) 2017: 0.592

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 12, Issue 3


On the Benford's Empirical Law

Stanislav Molchanov / Xian Wang

The paper contains the mathematical analysis of the so-called Benford's Empirical Law, closely related to the famous Weil's theorem about uniform distribution on [0,1] of the sequence of the fractional parts xn = {n α}, α is an irrational number, and Poincaré theorem about convolutions of the measures on the group S 1 = [0, 1)mod 1 . We prove that the Weil's theorem is "robust" in appropriate sense and generalize the Poincaré theorem for the class of dependent random variables.

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Published in Print: 2004-09-01

Citation Information: Random Operators and Stochastic Equations rose, Volume 12, Issue 3, Pages 201–210, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/1569397042222495.

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