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On the Variance of Additive Random Variables on Stochastic Polyhedra

  • Let \(a_i i:= 1,\dots,m.\) be an i.i.d. sequence taking values in \(\mathbb{R}^n\). Whose convex hull is interpreted as a stochastic polyhedron \(P\). For a special class of random variables which decompose additively relative to their boundary simplices, eg. the volume of \(P\), integral representations of their first two moments are given which lead to asymptotic estimations of variances for special "additive variables" known from stochastic approximation theory in case of rotationally symmetric distributions.

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Author:Karl-Heinz Küfer
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50521
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (233)
Document Type:Report
Language of publication:English
Publication Date:2017/11/09
Year of Publication:1992
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/09
Number of page:29
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)