Vol. 28, No. 1, 1969

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On the decomposition of infinitely divisible probability laws without normal factor

Roger Cuppens

Vol. 28 (1969), No. 1, 61–76

In the theory of the decomposition of probability laws, the fundamental problem stated by D. A. Raikov of the characterization of the class I0 of the infinitely divisible laws without indecomposable factors has been studied in the case of univariate laws by Yu. V. Linnik and I. V. Ostrovskiy. Lately, we have shown that nearly all these results can be extended to the case of multivariate laws. In this paper, we give a result which can be considered as an extension of a theorem of Raikov and P. Lévy and of a particular case of theorems of Linnik, and the extension of this result to the case of several variables.

Mathematical Subject Classification
Primary: 60.20
Received: 20 December 1967
Published: 1 January 1969
Roger Cuppens