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On the moment determinacy of the distributions of compound geometric sums

Part of: Integral transforms, operational calculus Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Gwo Dong Lin  and
Jordan Stoyanov
Gwo Dong Lin*
Affiliation:
Academia Sinica, Taiwan
Jordan Stoyanov*
Affiliation:
University of Newcastle upon Tyne
*
∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, Republic of China. Email address: gdlin@stat.sinica.edu.tw
∗∗ Postal address: School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK.
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Abstract

We deal with compound geometric sums of independent positive random variables and study the moment problem for the distributions of such sums (the Stieltjes moment problem). We find conditions under which the distributions are uniquely determined by their moments. We also treat related topics, including the Hamburger moment problem involving random variables on the whole real line. Some conjectures are outlined.

Keywords

Compound geometric summomentsdeterminate and indeterminate moment problemsCarleman criterionKrein criterionLin condition

MSC classification

Primary: 60E05: Distributions 44A60: Moment problems
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 545 - 554
Copyright
Copyright © Applied Probability Trust 2002 

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