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Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 4, Pages 725–745 (Mi tvp5304)  

On conditions under which a probability distribution is uniquely determined by its moments

E. B. Yarovayaa, J. Stoyanovb, K. K. Kostyashinc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
c Lomonosov Moscow State University

Abstract: We study the relationship between the well-known Carlemans condition which guarantees uniqueness of determination of a probability distribution by its moments and a recent and easily checkable condition on the rate of growth of the moments. We use asymptotic methods in theory of integrals and involve properties of Lamberts W-function to show that the rate of growth of the ratios of consecutive moments, as a sufficient condition for uniqueness, is more demanding than Carlemans condition. We establish other results, one of them showing that Carlemans condition does not follow from Hardys condition, although the reverse implication is true. Related topics are also discussed.

Keywords: random variables, moment problem, M-determinacy, Carlemans condition, rate of growth of the moments, Hardys condition, Lambert W-function.

Funding Agency Grant Number
Russian Science Foundation 19-11-00290


DOI: https://doi.org/10.4213/tvp5304

Full text: PDF file (563 kB)
First page: PDF file
References: PDF file   HTML file

MSC: 60E05, 62E10, 44A60
Received: 16.05.2019
Revised: 09.07.2019
Accepted:18.07.2019

Citation: E. B. Yarovaya, J. Stoyanov, K. K. Kostyashin, “On conditions under which a probability distribution is uniquely determined by its moments”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 725–745

Citation in format AMSBIB
\Bibitem{YarStoKos19}
\by E.~B.~Yarovaya, J.~Stoyanov, K.~K.~Kostyashin
\paper On conditions under which a probability distribution is uniquely determined by its moments
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 4
\pages 725--745
\mathnet{http://mi.mathnet.ru/tvp5304}
\crossref{https://doi.org/10.4213/tvp5304}


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  •     Theory of Probability and its Applications
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