Abstract:
We have analyzed some conditions which are essentially involved in deciding
whether or not a probability distribution is unique (moment-determinate) or
nonunique (moment-indeterminate) by its moments. We suggest new
conditions concerning both absolutely continuous and discrete distributions. By
using the new conditions, which are easily checkable, we either establish new
results or extend previous ones in both the Hamburger case (distributions on the
whole real line) and the Stieltjes case (distributions on the positive
half-line). Specific examples illustrate the results as well as the relationship
between the new conditions and previously available conditions.
Keywords:probability distributions, moments, Stieltjes moment problem, Hamburger moment problem, Carleman's condition, Krein's condition, condition (L).
Citation:
J. M. Stoyanov, G. D. Lin, P. Kopanov, “New checkable conditions for moment determinacy of probability distributions”, Teor. Veroyatnost. i Primenen., 65:3 (2020), 634–648; Theory Probab. Appl., 65:3 (2020), 497–509
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\by J.~M.~Stoyanov, G.~D.~Lin, P.~Kopanov
\paper New checkable conditions for moment determinacy of probability distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 2020
\vol 65
\issue 3
\pages 634--648
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\crossref{https://doi.org/10.4213/tvp5278}
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\jour Theory Probab. Appl.
\yr 2020
\vol 65
\issue 3
\pages 497--509
\crossref{https://doi.org/10.1137/S0040585X97T990083}
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Linking options:
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https://doi.org/10.4213/tvp5278
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