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- W2040967539 abstract "For -1 < β < 0, subclasses, U β, of the Lévy class L o of selfdecomposable measures on Banach spaces, are examined. They are defined as limit distributions in certain summation schemes. The main result in Section 1 (Theorem 1.2) shows that each measure μi from Uβ is a convolution of a strictly stable measure with exponent (-β) and a probability distribution of random integral $$int_{(0,1)}tdY(t^{beta})$$ , where Y is a Lévy process with finite (-β)th moment. The situation differs essentially from that with positive U β Theorem 2.2 (in Section 2) shows that the natural mapping $$pounds (Y(1))to pounds(int_{(0,1)}tdY(t^{beta}))$$ is a homeomorphism, which immediately gives so called “generators” for the classU β In addition, potential applications of measures from Uβ in the Ising model for ferromagnetism are indicated. Finally, Remark 3.B shows that the classes U β constitute a filtration of the semigroup ID of all infinitely divisible measures." @default.
- W2040967539 created "2016-06-24" @default.
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- W2040967539 date "1992-01-01" @default.
- W2040967539 modified "2023-10-18" @default.
- W2040967539 title "Random Integral Representations for Classes of Limit Distributions Similar to Levy Class L 0. III" @default.
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- W2040967539 doi "https://doi.org/10.1007/978-1-4612-0367-4_10" @default.
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