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Factorization theory for probability distributions. (English) Zbl 0833.60016

This is the written version of a lecture presented by the author. It concerns contributions of H. Cramér to the theory of factorization of probability distributions, and related subjects. The best known results in this area are the theorems named after Cramér (for normal distributions) and Raikov (for Poisson distributions). A brief overview is given of results on indecomposable factors; brief sketches of a few proofs are given. Some results of Linnik and Ostrovskij are discussed in relation to Cramér’s work. The final section concerns some more recent developments in infinite divisibility; results by Goldie and the reviewer, by Thorin, by the author himself, and most recently by G. K. Kristiansen [Ann. Probab. 22, No. 1, 442-452 (1994; Zbl 0796.60017)] who proved an old conjecture of mine.

MSC:

60E05 Probability distributions: general theory
60E07 Infinitely divisible distributions; stable distributions
60E10 Characteristic functions; other transforms

Citations:

Zbl 0796.60017
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Full Text: DOI

References:

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