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The Truncated Moment Problem on N0

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2017

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Kuna, Tobias
Lebowitz, Joel L.
Speer, Eugene R.

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https://doi.org/10.1016/j.jmaa.2017.02.060
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http://arxiv.org/abs/1504.02989v2

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Journal of Mathematical Analysis and Applications. 2017, 452(1), pp. 443-468. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2017.02.060

Zusammenfassung

We find necessary and sufficient conditions for the existence of a probability measure on N0, the nonnegative integers, whose first n moments are a given n-tuple of nonnegative real numbers. The results, based on finding an optimal polynomial of degree n which is nonnegative on N0 (and which depends on the moments), and requiring that its expectation be nonnegative, generalize previous results known for n=1, n=2 (the Percus-Yamada condition), and partially for n=3. The conditions for realizability are given explicitly for n ≤ 5 and in a finitely computable form for n ≥ 6. We also find, for all n, explicit bounds, in terms of the moments, whose satisfaction is enough to guarantee realizability. Analogous results are given for the truncated moment problem on an infinite discrete semi-bounded subset of R.

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510 Mathematik

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truncated moment problem; discrete moment problem; realizability

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ISO 690INFUSINO, Maria, Tobias KUNA, Joel L. LEBOWITZ, Eugene R. SPEER, 2017. The Truncated Moment Problem on N0. In: Journal of Mathematical Analysis and Applications. 2017, 452(1), pp. 443-468. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2017.02.060
BibTex
@article{Infusino2017Trunc-33286,
  year={2017},
  doi={10.1016/j.jmaa.2017.02.060},
  title={The Truncated Moment Problem on N<sub>0</sub>},
  number={1},
  volume={452},
  issn={0022-247X},
  journal={Journal of Mathematical Analysis and Applications},
  pages={443--468},
  author={Infusino, Maria and Kuna, Tobias and Lebowitz, Joel L. and Speer, Eugene R.}
}
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