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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Further comments on the continuity of distribution functions obtained by superposition


Author: Barthel W. Huff
Journal: Proc. Amer. Math. Soc. 35 (1972), 561-564
MSC: Primary 60E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0303574-7
MathSciNet review: 0303574
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Abstract: Let $ \{ X(t)\} $ be a differential process with discontinuous distributions and Y a nonnegative random variable independent of the process. The superposition $ X(Y)$ has a continuous probability distribution if and only if the process has nonzero trend term and Y has continuous distribution. The nature of discontinuities of the probability distribution of the superposition is indicated.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0303574-7
Keywords: Superposition, differential process, trend term, Lévy spectral function, random sum
Article copyright: © Copyright 1972 American Mathematical Society