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A moment problem

Published online by Cambridge University Press:  09 April 2009

Lajos Takács
Lajos Takács
Affiliation:
Department of Mathematical Statistics, Columbia University
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Let ν be a discrete random variable taking on nonnegative integer values and set P{ν = κ} = Pk, κ = 0, 1, hellip. Suppose that the binomial moments are finite. Frequently the problem arises under what conditions the probabilities Pk, k = 0, 1,…, can be determined uniquely by the sequence of moments Br, r = 0, 1,…, and how it can be done.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 4 , November 1965 , pp. 487 - 490
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Doveretzky, A. (1963) On an elementary identity in the theory of probability. Columbia University Report, 11 13, 1963.Google Scholar
[2]Hardy, G. H. (1949) Divergent Series. Oxford University Press.Google Scholar
[3]Jordon, K. (1927) A valószinüségszámitás alapfogalmai. (Les fondements du calcul des probabilitiés.) Mathematikai és Physikai Lapok 34 109–136.Google Scholar
[4]Jordon, ch. (1934) Le théorème de probailité de Poincaré, généralisé au cas de plusieurs variables indépendantes, Acta Sci. Math. (Szeged) 7, 103–111.Google Scholar
[5]Jordon, Ch (1939) Problémes de la probabilité des épreuves répétées dans le cas général. Bull. de la Société Mathématique de France 67, 223–242.CrossRefGoogle Scholar
[6]Knopp, K. (1923) Über das Eulersche Summierungsverfahren I-II Mathem. Zeitschr. 15 (1922), 226–253 and 18 1923, 125–156.CrossRefGoogle Scholar
[7]Poincaré, H., (1896) Calcul des probabilités. Gauthier-Villars, Paris.Google Scholar
[8]Takács, L. (1958) On a general probability theorem and its applications in the theory of stochastic processes. Proc. Soc. Cambridge Phil. Soc. 54, 219–224.CrossRefGoogle Scholar