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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 4, Pages 787–797 (Mi tvp5126)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Any random variable with finite moments is a sum of two variables with determinate moment problem

K. V. Lykovab

a Image Processing Systems Institute of the RAS - Branch of the FSRC "Crystallography and Photonics" RAS, Samara, Russia, Samara
b Samara National Research University

Abstract: It is known that two random variables may have equal moments of all orders but unequal distributions. If, for a given random variable, there does not exist a differently distributed random variable with the same moments, then the original random variable is said to have determinate moment problem, or one says that the moment problem has a unique solution. It is shown that any random variable such that all its moments are finite can be represented as a sum of two disjoint variables, and each of them has determinate moment problem.

Keywords: Hamburger moment problem, Carleman condition, mixture of distributions, Orlicz space.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31452-мол_а
Ministry of Education and Science of the Russian Federation 02.B49.21.0005
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant 14-01-31452_mol_a) and the Ministry of Education and Science of the Russian Federation in the framework of enhancing the competitive ability of Samara University (agreement 02.B49.21.0005).


DOI: https://doi.org/10.4213/tvp5126

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English version:
Theory of Probability and its Applications, 2018, 62:4, 632–639

Bibliographic databases:

Received: 11.11.2015
Revised: 02.06.2016

Citation: K. V. Lykov, “Any random variable with finite moments is a sum of two variables with determinate moment problem”, Teor. Veroyatnost. i Primenen., 62:4 (2017), 787–797; Theory Probab. Appl., 62:4 (2018), 632–639

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. B. Yarovaya, J. Stoyanov, K. K. Kostyashin, “On conditions for a probability distribution to be uniquely determined by its moments”, Theory Probab. Appl., 64:4 (2019), 579–594  mathnet  crossref  crossref  isi  elib
    2. J. M. Stoyanov, G. D. Lin, P. Kopanov, “New checkable conditions for moment determinacy of probability distributions”, Teoriya veroyatn. i ee primen., 65:3 (2020), 634–648  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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