Jordan M. Stoyanov

Jan 30, 2024 | mdpi.com | Jordan M. Stoyanov |Aldo Tagliani |Novi Inverardi |Pier Luigi

1. IntroductionWhen studying probability distributions, one of the challenging questions we arrive at comes from the classical moment problem. The question is whether or not a probability distribution is uniquely determined by the sequence of all moments, assuming they are finite. The answer can be given for the distribution itself; equivalently, for the associated random variable X; its distribution function F; the density f=F′; or the bounded positive measure μ=μF induced by F.

Sep 11, 2023 | mdpi.com | Pier Luigi |Aldo Tagliani |Jordan M. Stoyanov |Novi Inverardi

1.4. About the Novelties in Our ApproachCrucial in our approach is to exploit the following:The geometric interpretation of the indeterminacy conditions as developed by Merkes-Wetzel [21]. Properties of the eigenvalues of perturbed symmetric matrices in the spirit of Golub-Van Loan [22] and Wilkinson [23]. Both these are among the novelties in our exposition.