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Lookup NU author(s): Dr Jordan Stoyanov
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In 1944 M.G. Krein proposed a condition throwing light on the moment problem for absolutely continuous probability distributions. This condition, implying non-uniqueness, is expressed in terms of a normalized logarithmic integral of the density and has different forms in the Hamburger moment problem (for distributions on the whole real line) and in the Stieltjes moment problem (for distributions on the positive real line). Other forms of the Krein condition, together with new conditions (smoothing and growth condition on the density) suggested by G.D. Lin and based on a work by H. Dym and H.P. McKean, led to a unique solution to the moment problem. We present new results, give new proofs of previously known results and discuss related topics. © 2000 ISI/BS.
Author(s): Stoyanov J
Publication type: Article
Publication status: Published
Journal: Bernoulli
Year: 2000
Volume: 6
Issue: 5
Pages: 939-949
ISSN (print): 1350-7265
ISSN (electronic): 1573-9759
Publisher: International Statistical Institute
URL: http://dx.doi.org/10.2307/3318763
DOI: 10.2307/3318763
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