Article PDF
References
Baxter, G., Shapiro, J.M.: On bounded infinitely divisible random variables. Sankhyā 22, 253–260 (1960)
Feller, W.: An introduction to probability theory and its applications. Vol. II. 2nd ed. New York: Wiley 1971
Fukushima, M.: On the spectral distribution of a disordered system and the range of a random walk. Osaka J. Math. 11, 73–85 (1974)
Gnedenko, B.V., Kolmogorov, A.N.: Limit distributions for sums of independent random variables. 2nd ed. Reading: Addison-Wesley 1968
Ibragimov, I.A., Linnik, Ju.V.: Independent and stationary sequences of random variables. Groningen: Wolters-Noordhoff 1971
Johnson, N.L., Rogers, C.A.: The moment problem for unimodal distributions. Ann. Math. Statist. 22, 433–439 (1951)
Kruglov, V.M.: A note on infinitely divisible distributions. Theor. Probability Appl. 15, 319–324 (1970)
Lévy, P.: Théorie de l'addition des variables aleatoires. Paris: Gauthier-Villars 1937 (2e ed. 1954)
Minlos, R.A., Povzner, A.Ja.: Thermodynamic limit for entropy. (In Russian). Trudy Moskov. Mat. Obšč. 17, 243–272 (1967)
Steutel, F.W.: Preservation of infinite divisibility under mixing and related topics. Math. Centre Tracts 33 (Math. Centre, Amsterdam, 1970)
Urbanik, K.: A representation of self-decomposable distributions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16, 209–214 (1968)
Wolfe, S.J.: On the unimodality of L functions. Ann. Math. Statist. 42, 912–918 (1971)
Wolfe, S.J.: On the continuity properties of L functions. Ann. Math. Statist. 42, 2064–2073 (1971)
Wolfe, S.J.: Inequalities for modes of L functions. Ann. Math. Statist. 42, 2126–2130 (1971)
Yamazato, M.: Some results on infinitely divisible distributions of class L with applications to branching processes. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 13, 133–139 (1975)
Yamazato, M.: Unimodality of infinitely divisible distribution functions of class L. Ann. Probability 6, No. 4 (To appear August, 1978)
Zolotarev, V.M.: The analytic structure of infinitely divisible laws of class L. (In Russian). Litovsk. Mat. Sb. 3, 123–140 (1963)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sato, Ki., Yamazato, M. On distribution functions of class L . Z. Wahrscheinlichkeitstheorie verw Gebiete 43, 273–308 (1978). https://doi.org/10.1007/BF00534763
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00534763