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.
Author: | Karl-Heinz Küfer |
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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) |