Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T17:21:23.046Z Has data issue: false hasContentIssue false

On the moment problem for random sums

Published online by Cambridge University Press:  14 July 2016

Allan Gut*
Affiliation:
Uppsala University
*
Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden. Email address: [email protected]

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.

MSC classification

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berg, C. (1985). On the preservation of determinacy under convolution. Proc. Amer. Math. Soc. 93, 351357.Google Scholar
Devinatz, A. (1959). On a theorem of Lévy-Raikov. Ann. Math. Statist. 30, 583586.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, 545554.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, 101111.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, 247254.CrossRefGoogle Scholar