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April, 1975 Decomposition of Functions of Bounded Variation
Gary L. Grunkemeier
Ann. Probab. 3(2): 329-337 (April, 1975). DOI: 10.1214/aop/1176996403

Abstract

Cramer's theorem, that a normal distribution function $(\operatorname{df})$ has only normal components, is extended to a case where the components are allowed to be from a subclass $(B_1)$ of the functions of bounded variation other than the class of df's. One feature of $B_1$ is that it contains more of the df's than the classes for which previous similar extensions have been made; in particular it contains the Poisson df's so that a first extension of Raikov's theorem, that a Poisson df has only Poisson components, in the same direction, is also given.

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Gary L. Grunkemeier. "Decomposition of Functions of Bounded Variation." Ann. Probab. 3 (2) 329 - 337, April, 1975. https://doi.org/10.1214/aop/1176996403

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0325.60017
MathSciNet: MR372942
Digital Object Identifier: 10.1214/aop/1176996403

Subjects:
Primary: 60E05
Secondary: 42A72 , 42A96

Keywords: Bounded variation , Cramer's theorem , Decomposition , Fourier-Stieltjes transform , Raikov's theorem

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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