Summary
The problem of characterizing the infinitely divisible characteristic functions which have only infinitely divisible factors is considered. Under the assumption that both the absolutely continuous and the singular (or the discrete) components exist in Poisson spectral measures, several necessary conditions for this problem are obtained. These conditions admit partial converses and new examples of infinitely divisible characteristic functions which have only infinitely divisible factors are given.
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Mase, S. Decomposition of infinitely divisible characteristic functions without Gaussian component. Ann Inst Stat Math 29, 275–286 (1977). https://doi.org/10.1007/BF02532789
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DOI: https://doi.org/10.1007/BF02532789