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Self-decomposability on ℝ and ℤ

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1064)

Abstract

The set L(ℝ) of self-decomposable probability measures on ℝ is studied in terms of characteristic functions using a certain differential operator and its inverse. In particular a natural bijection onto L(ℝ), introduced by Wolfe, is interpreted via these operators.

In a similar way a bijection of certain sets of probability measures on ℤ is discussed, and this leads to a notion of discrete self-decomposability on ℤ which extends the notion of discrete self-decomposability on ℤ+ as defined by Steutel and van Harn.

Keywords

  • Probability Measure
  • Discrete Analogue
  • Pointwise Limit
  • Natural Bijection
  • Infinite Divisibility

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Berg, C. and G. Forst: Multiply self-decomposable probability measures on ℝ+ and ℤ+. Z. Wahrscheinlichkeitstheorie verw. Gebiete 62, 147–163 (1983).

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© 1984 Springer-Verlag

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Forst, G. (1984). Self-decomposability on ℝ and ℤ. In: Heyer, H. (eds) Probability Measures on Groups VII. Lecture Notes in Mathematics, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073637

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  • DOI: https://doi.org/10.1007/BFb0073637

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13341-4

  • Online ISBN: 978-3-540-38874-6

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