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Decomposition problem of probability measures related to monotone regularly varying functions

Published online by Cambridge University Press:  22 January 2016

Takaaki Shimura
Takaaki Shimura*
Affiliation:
The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106, Japan
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This paper deals with a decomposition problem for some classes of distributions. Let D be a given class of distribution on R1, which we are interested in. After showing that the class D is closed under convolution, our purpose is to give an answer to the inverse problem: if the convolution of two distributions μ1 and (μ2 belongs to D, then do μ1 and μ2 belong to D?

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 135 , September 1994 , pp. 87 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

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