Summary
Throughout this paper the symbols r.v., d.f., ch.f., and i.d. will stand, respectively, for “random variable”, “distribution function”, “characteristic function”, and “infinitely divisible”.
Let F(x) be an i.d.d.f. Hartman and Wintner [5] and Blum and Rosenblatt [1] have given a condition, necessary and sufficient, for F(x) to be a continuous d.f. In this note a sufficient condition for F(x) to be an absolutely continuous d.f. is given.
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References
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Research supported by ONR Contract No. NONR-285(46).
Research supported in part by a National Science Foundation fellowship.
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Fisz, M., Varadarajan, V.S. A condition for absolute continuity of infinitely divisible distribution functions. Z. Wahrscheinlichkeitstheorie verw Gebiete 1, 335–339 (1963). https://doi.org/10.1007/BF00533408
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DOI: https://doi.org/10.1007/BF00533408