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Matematicheskie Zametki, 2012, Volume 91, Issue 1, Pages 79–92
DOI: https://doi.org/10.4213/mzm8762
(Mi mzm8762)
 

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

Some Remarks on the Moment Problem and Its Relation to the Theory of Extrapolation of Spaces

K. V. Lykov

Samara State University
Full-text PDF (503 kB) Citations (2)
References:
Abstract: It is well known that that the coincidence of integer moments ($n$th-power moments, where $n$ is an integer) of two nonnegative random variables does not imply the coincidence of their distributions. Moreover, we show that, given coinciding integer moments, the ratio of half-integer moments may tend to infinity arbitrarily fast. Also, in this paper, we give a new proof of uniqueness in the continuous moment problem and show that, in that problem, it is impossible to replace the condition of coincidence of all moments by a two-sided inequality between them, while preserving the inequality between the distributions. In conclusion, we study the relationship with the theory of extrapolation of spaces.
Keywords: nonnegative random variable, distribution function, integer moment, half-integer moment, continuous moment problem, extrapolation of spaces, Lebesgue measure, Orlicz space.
Received: 11.05.2010
Revised: 16.01.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 1, Pages 69–80
DOI: https://doi.org/10.1134/S0001434612010087
Bibliographic databases:
Document Type: Article
UDC: 519.213+517.98
Language: Russian
Citation: K. V. Lykov, “Some Remarks on the Moment Problem and Its Relation to the Theory of Extrapolation of Spaces”, Mat. Zametki, 91:1 (2012), 79–92; Math. Notes, 91:1 (2012), 69–80
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm8762
  • https://www.mathnet.ru/eng/mzm/v91/i1/p79
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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