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Short Communications
The class $I_0$ for random increasing upper semicontinuous functions
D. Neuenschwander Université de Lausanne, Ecole des Hautes Etudes Commerciales, Institut de Sciences Actuarielles, Suisse
Abstract:
Let $C$ be the convex cone $USC_*([0,1],\mathbf{R}_+)$ of increasing upper semicontinuous functions $g\colon[0,1]\to\mathbf{R}_+$. It is shown that the class $I_0(C)$ of distributions on $C$ without indecomposable factor is strictly included in the class of infinitely divisible distributions on $C$.
Keywords:
probability measures without indecomposable factor, upper semicontinuous function, infinitely divisible distributions.
Received: 17.02.1998
Citation:
D. Neuenschwander, “The class $I_0$ for random increasing upper semicontinuous functions”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 148–151; Theory Probab. Appl., 44:1 (2000), 106–109
Linking options:
https://www.mathnet.ru/eng/tvp612https://doi.org/10.4213/tvp612 https://www.mathnet.ru/eng/tvp/v44/i1/p148
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