The Moment Problem

By A. Gut. Encyclopedia of Special Functions: The Askey-Bateman Project, 2002

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The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the theory of regularly varying functions. In particular, two questions addressed in a recent paper by Stoyanov concerning powers of random variables and functions that (do not) preserve uniqueness will be investigated.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics

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