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- W2008173677 abstract "In this paper we introduce and study a regularizing one-to-one mapping ϒ0 from the class of one-dimensional Lévy measures into itself. This mapping appeared implicitly in our previous paper [O.E. Barndorff-Nielsen, S. Thorbjørnsen, A connection between free and classical infinite divisibility, Inf. Dim. Anal. Quant. Probab. 7 (2004) 573–590], where we introduced a one-to-one mapping ϒ from the class ID(*) of one-dimensional infinitely divisible probability measures into itself. Based on the investigation of ϒ0 in the present paper, we deduce further properties of ϒ . In particular it is proved that ϒ maps the class L(*) of selfdecomposable laws onto the so called Thorin class T(*). Further, partly motivated by our previous studies of infinite divisibility in free probability, we introduce a one-parameter family (ϒα)α∈[0,1] of one-to-one mappings ϒα:ID(*)→ID(*), which interpolates smoothly between ϒ (α=0) and the identity mapping on ID(*) (α=1). We prove that each of the mappings ϒα shares many of the properties of ϒ. In particular, they are representable in terms of stochastic integrals with respect to associated Levy processes." @default.
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- W2008173677 date "2006-03-01" @default.
- W2008173677 modified "2023-10-11" @default.
- W2008173677 title "Regularizing mappings of Lévy measures" @default.
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- W2008173677 doi "https://doi.org/10.1016/j.spa.2005.09.011" @default.
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