Geodesic
Any random variable with finite moments is a sum of two variables with determinate moment problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 787-797 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, mixture of distributions, Orlicz space.
Mots-clés : Carleman condition 
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K. V. Lykov. Any random variable with finite moments is a sum of two variables with determinate moment problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 787-797. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a7/

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