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On the moment problem for random sums

Part of:Distribution theory - ProbabilityIntegral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Allan Gut
Allan Gut*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden. Email address: allan.gut@math.uu.se
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Abstract

A recent paper by Lin and Stoyanov is devoted to the moment problem for geometrically compounded sums. The aim of this note is to provide affirmative answers to their conjectures.

Keywords

Moment problemuniquenessrandom sumCarleman conditionLin conditionstopping time

MSC classification

Primary:60E05: Distributions
Secondary:44A60: Moment problems

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003, pp. 797 - 802
Copyright
Copyright © Applied Probability Trust 2003 

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References

Berg, C. (1985). On the preservation of determinacy under convolution. Proc. Amer. Math. Soc. 93, 351–357.Google Scholar
Devinatz, A. (1959). On a theorem of Lévy-Raikov. Ann. Math. Statist. 30, 583–586.Google Scholar
Gut, A. (1988). Stopped Random Walks. Springer, New York.CrossRefGoogle Scholar
Lin, G.D., and Stoyanov, J. M. (2002). On the moment determinacy of the distributions of compound geometric sums. J. Appl. Prob. 39, 545–554.CrossRefGoogle Scholar
Pakes, A. G., Hung, W.-L., and Wu, J.-W. (2001). Criteria for the unique determination of probability distributions by moments. Austral. N. Z. J. Statist. 43, 101–111.CrossRefGoogle Scholar
San Juan, R. (1943). Sur le problème de Watson dans la théorie des séries asymptotiques et solution d'un problème de Carleman de la théorie des fonctions quasianalythiques. Acta Math. 75, 247–254.CrossRefGoogle Scholar