On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuous
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- by Howard G. Tucker PDF
- Trans. Amer. Math. Soc. 118 (1965), 316-330 Request permission
References
- J. R. Blum and Murray Rosenblatt, On the structure of infinitely divisible distributions, Pacific J. Math. 9 (1959), 1–7. MR 105729
- Marek Fisz, Infinitely divisible distributions: recent results and applications, Ann. Math. Statist. 33 (1962), 68–84. MR 139188, DOI 10.1214/aoms/1177704712
- M. Fisz and V. S. Varadarajan, A condition for absolute continuity of infinitely divisible distribution functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1962/63), 335–339. MR 149521, DOI 10.1007/BF00533408
- B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR 0062975
- Philip Hartman and Aurel Wintner, On the infinitesimal generators of integral convolutions, Amer. J. Math. 64 (1942), 273–298. MR 6635, DOI 10.2307/2371683
- Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
- Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
- Eugene Lukacs, Characteristic functions, Griffin’s Statistical Monographs & Courses, No. 5, Hafner Publishing Co., New York, 1960. MR 0124075 H. Rubin, Supports of infinitely divisible distributions, Tech. Rep. No. RM-108 HR-10, Michigan State Univ., Department of Statistics, East Lansing, Mich., 1963.
- Howard G. Tucker, Absolute continuity of infinitely divisible distributions, Pacific J. Math. 12 (1962), 1125–1129. MR 146868
- Howard G. Tucker, On continuous singular infinitely divisible distribution functions, Ann. Math. Statist. 35 (1964), 330–335. MR 161362, DOI 10.1214/aoms/1177703755
Additional Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 118 (1965), 316-330
- MSC: Primary 60.20
- DOI: https://doi.org/10.1090/S0002-9947-1965-0182061-4
- MathSciNet review: 0182061