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.
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References
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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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