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Some recent results in infinite divisibility

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  • Steutel, F. W.

Abstract

In this paper, a survey is given of some recent developments in infinite divisibility. There are three main topics: (i) the occurrence of infinitely divisible distributions in applied stochastic processes such as queueing processes and birth-death processes, (ii) the construction of infinitely divisible distributions, mainly by mixing, and (iii) conditions for infinite divisibility in terms of distribution functions and densities.

Suggested Citation

  • Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    • Handle: RePEc:eee:spapps:v:1:y:1973:i:2:p:125-143
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    Cited by:

    1. Lennart Bondesson, 2002. "On the Lévy Measure of the Lognormal and the LogCauchy Distributions," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 243-256, September.
    2. Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.
    3. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    4. Lennart Bondesson, 2015. "A Class of Probability Distributions that is Closed with Respect to Addition as Well as Multiplication of Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1063-1081, September.

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