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Asymptotic ordering of distribution functions and convolution semigroups

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Abstract

It is well-known that the setH of distribution functions on [0,∞] supplied with the convolution product * is a semigroup. We introduce a preorder on (H,*) with attractive algebraic properties. The corresponding equivalence relation ≈W extends the concept of tail-equivalence of distribution functions. We show that the idempotents of the factorsemigroupH W form a subsemigroup ofH W.

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  1. Seminar für Statistik, Universität Mannheim, D-6800, Mannheim, Federal Republic of Germany

    Claudia Klüppelberg

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  1. Claudia Klüppelberg
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communicated by K.H. Hofmann

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Klüppelberg, C. Asymptotic ordering of distribution functions and convolution semigroups. Semigroup Forum 40, 77–92 (1990). https://doi.org/10.1007/BF02573252

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  • DOI: https://doi.org/10.1007/BF02573252

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