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Krein condition in probabilistic moment problems
Jordan Stoyanov
Source: Bernoulli Volume 6, Number 5
(2000), 939-949.
Abstract
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.
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Keywords: determinate probability distributions; Hamburger moment problem; indeterminate probability distributions; Krein condition; Lin condition; moment sequence; powers of distributions; Stieltjes moment problem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1081282696
Mathematical Reviews number (MathSciNet): MR2001i:44014
Zentralblatt MATH identifier: 0971.60017
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