Geodesic
On conditions for a probability distribution to be uniquely determined by its moments
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 725-745 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent, easily checkable condition on the rate of growth of the moments. We use asymptotic methods in the theory of integrals and involve properties of the Lambert $W$-function to show that the quadratic growth rate of the ratios of consecutive moments as a sufficient condition for uniqueness is slightly more restrictive than Carleman's condition. We derive a series of statements, one of which shows that Carleman's condition does not imply Hardy's condition, although the inverse implication is true. Related topics are also discussed.
Mots-clés : random variables, Carleman's condition
Keywords: moment problem, M-determinacy, rate of growth of the moments, Hardy's condition, Lambert $W$-function. 
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E. B. Yarovaya; J. Stoyanov; K. K. Kostyashin. On conditions for a probability distribution to be uniquely determined by its moments. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 725-745. http://geodesic.mathdoc.fr/item/TVP_2019_64_4_a5/

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