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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Further comments on the continuity of distribution functions obtained by superposition
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by Barthel W. Huff
Proc. Amer. Math. Soc. 35 (1972), 561-564
DOI: https://doi.org/10.1090/S0002-9939-1972-0303574-7

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.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • 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