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- W126809045 abstract "Given a sequence (C, T) = (C, T 1, T 2, …) of real-valued random variables, the associated so-called smoothing transform (mathcal{S}) maps a distribution F from a subset Γ of distributions on (mathbb{R}) to the distribution of (sum _{igeq 1}T_{i}X_{i} + C), where X 1, X 2, … are iid with common distribution F and independent of (C, T). This review aims at providing a comprehensive account of contraction properties of (mathcal{S}) on subsets Γ specified by the existence of moments up to a given order like, for instance, ({mathcal{P}}^{p}(mathbb{R}) ={ F:int vert x{vert }^{p},F(dx) 0 or (mathcal{P}_{c}^{p}(mathbb{R}) ={ F in {mathcal{P}}^{p}(mathbb{R}):int x,F(dx) = c}) for p ≥ 1. The metrics used here are the minimal l p -metric and the Zolotarev metric ζ p , both briefly introduced in Sect. 3." @default.
- W126809045 created "2016-06-24" @default.
- W126809045 creator A5090566468 @default.
- W126809045 date "2013-01-01" @default.
- W126809045 modified "2023-09-23" @default.
- W126809045 title "The Smoothing Transform: A Review of Contraction Results" @default.
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- W126809045 doi "https://doi.org/10.1007/978-3-642-38806-4_9" @default.
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