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Decomposition of infinitely divisible characteristic functions with absolutely continuous poisson spectral measure

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Abstract

We shall consider the problem of characterizing infinitely divisible characteristic functions which have only infinitely divisible factors. Infinitely divisible characteristic functions treated in this paper are those which have absolutely continuous Poisson spectral measures and have no Gaussian component in their Lévy canonical representations. It will be shown that Ostrovskii's sufficient condition is also necessary in this case.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Shigeru Mase

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  1. Shigeru Mase
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Mase, S. Decomposition of infinitely divisible characteristic functions with absolutely continuous poisson spectral measure. Ann Inst Stat Math 27, 289–298 (1975). https://doi.org/10.1007/BF02504648

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  • DOI: https://doi.org/10.1007/BF02504648

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