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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Metadaten
Author:Karl-Heinz Küfer
URN:urn:nbn:de:hbz:386-kluedo-50521
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (233)
Document Type:Report
Language of publication:English
Date of Publication (online):2017/11/09
Year of first Publication:1992
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/09
Page Number:29
Faculties / Organisational entities:Kaiserslautern - 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)