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A survey of the theory of characteristic functions

Published online by Cambridge University Press:  01 July 2016

Eugene Lukacs
Eugene Lukacs*
Affiliation:
The Catholic University of America, Washington, D. C.
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Abstract

The paper gives a survey of the theory of univariate characteristic functions. These functions were originally introduced as tools in the study of limit theorems but it was later realized that they had an independent mathematical interest. Those parts of the theory which can be found in textbooks are treated only briefly; the main emphasis is placed on more recent developments and areas where active research is still in progress.

Keywords

UNIQUENESS, INVERSION, CONVOLUTION AND CONTINUITY THEOREMSINFINITE CONVOLUTIONANALYTIC AND BOUNDARY C. F.'SDECOMPOSMON OF C. F.'SINDECOMPOSABLE C.F.'SINFINITELY DIVISIBLE C.F.'SSTABLE LAWSTHE CLASS 10ALPHA DECOMPOSITIONSCHARACTERIZATION PROBLEMSSTABILITY THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 1 , April 1972 , pp. 1 - 37
Copyright
Copyright © Applied Probability Trust 1972 

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References

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