Classifying infinitely divisible distributions by functional equations

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

[1]  S. Wolfe,et al.  On Moments of Infinitely Divisible Distribution Functions , 1971 .

[2]  W. Vervaat.  On a stochastic difference equation and a representation of non–negative infinitely divisible random variables , 1979, Advances in Applied Probability.

[3]  Fw Fred Steutel,et al.  Discrete analogues of self-decomposability and stability , 1979 .

[4]  S. Wolfe,et al.  On the Unimodality of $L$ Functions , 1971 .

[5]  Marek Fisz,et al.  Infinitely Divisible Distributions: Recent Results and Applications , 1962 .

[6]  C. Berg,et al.  Infinitely divisible probability measures and potential kernels , 1979 .

[7]  F. Steutel.  Some recent results in infinite divisibility , 1973 .

[8]  D. Daley.  On a class of renewal functions , 1965, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  H. D. Miller.  A note on passage times and infinitely divisible distributions , 1967, Journal of Applied Probability.

[10]  Walter L. Smith.  Renewal Theory and its Ramifications , 1958 .

[11]  W. D. Warde,et al.  Infinite Divisibility of Discrete Distributions, II , 1971 .

[12]  E. C. Titchmarsh,et al.  The Laplace Transform , 1991, Heat Transfer 1.

[13]  B. Gnedenko,et al.  Limit Distributions for Sums of Independent Random Variables , 1955 .

[14]  J. Lamperti.  On the Coefficients of Reciprocal Power Series , 1958 .

[15]  F. Steutel,et al.  Generalized renewal sequences and infinitely divisible lattice distributions , 1977 .

[16]  Makoto Yamazato,et al.  Unimodality of Infinitely Divisible Distribution Functions of Class $L$ , 1978 .

[17]  J. Hawkes.  Intersections of Markov random sets , 1977 .

[18]  Emil Grosswald,et al.  The student t-distribution of any degree of freedom is infinitely divisible , 1976 .

[19]  Helly.  Aufgaben und Lehrsätze aus der Analysis , 1928 .

[20]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[21]  Some recent results in infinite divisibility , 1973, Advances in Applied Probability.

[22]  R. Horn,et al.  On multivariate infinitely divisible distributions , 1975 .

[23]  J. Hawkes,et al.  Infinitely divisible sequences , 1978 .

[24]  W. E. H. B.,et al.  Aufgaben und Lehrsätze aus der Analysis. , 1925, Nature.

[25]  H. Tucker.  On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuous , 1965 .

[26]  Douglas Kelker,et al.  Infinite Divisibility and Variance Mixtures of the Normal Distribution , 1971 .

[27]  H. Tucker.  Absolute continuity of infinitely divisible distributions. , 1962 .

[28]  K. Chung,et al.  Limit Distributions for Sums of Independent Random Variables. , 1955 .

[29]  D. Kendall.  Renewal sequences and their arithmetic , 1967 .

[30]  Ü Kuran,et al.  POTENTIAL THEORY ON LOCALLY COMPACT ABELIAN GROUPS , 1977 .

[31]  N. L. Johnson,et al.  Distributions in Statistics: Discrete Distributions. , 1970 .

[32]  F. Steutel,et al.  On the asymptotic behaviour of moments of infinitely dicisible distributions , 1977 .

[33]  J. Gurland,et al.  Some interrelations among compound and generalized distributions , 1957 .

[34]  Paul Erdös,et al.  Some Linear and Some Quadratic Recursion Formulas. I , 1951 .

[35]  P. Levy.  Théorie de l'addition des variables aléatoires , 1955 .

[36]  F. Steutel.  Preservation of infinite divisibility under mixing and related topics , 1972 .

[37]  V. Varadarajan,et al.  A condition for absolute continuity of infinitely divisible distribution functions , 1963 .

[38]  Y. Linnik,et al.  Decomposition of probability distributions , 1965, The Mathematical Gazette.

[39]  S. K. Katti.  Infinite Divisibility of Integer-Valued Random Variables , 1967 .

[40]  Theodor. Kaluza.  Über die Koeffizienten reziproker Potenzreihen , 1928 .