Further comments on the continuity of distribution functions obtained by superposition

Barthel W. Huff
1972 Proceedings of the American Mathematical Society  
Let {X(t)} be a differential process with discontinuous distributions and Y a nonnegative random variable independent of the process. The superposition A"( 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.
doi:10.1090/s0002-9939-1972-0303574-7 fatcat:y5wd35umlrem3appz5llt2j4pq