Analytische Fortsetzbarkeit von zufälligen Potenzreihen bezüglich abhängiger Zufallsvariabler. (Analytic continuability of random power series of dependent random variables)
type: Item
instance of: scholarly article
title: Analytische Fortsetzbarkeit von zufälligen Potenzreihen bezüglich abhängiger Zufallsvariabler. (Analytic continuability of random power series of dependent random variables)
zbMATH Open document ID: 0668.30003
DOI: 10.1007/BF02020759
author: Rolf Trautner
published in: Analysis Mathematica
publication date: 1988-01-01T00:00:00Z
review text: The author considers a sequence \(X=(X_ n(\omega))\) of random variables satisfying the condition \(E(X^ 4_ n)=O(1)\) (n\(\to \infty)\) and studies the corresponding random power series \(f_ x(z,\omega)=\sum^{\infty}_{n=0}a_ nX_ n(\omega)z^ n\). He proves analytic noncontinuability almost surely in the following cases: (i) for \(f_ x\) under the conditions of weak multiplicativity on X; (ii) for \(f_{\tilde X}\) where \(\tilde X=(\tilde X_ n)\) is a subsequence of X; (iii) at least for one of the series \(f_{x'}\) and \(f_{x''}\) where \(X'\) and \(X''\) are certain rearrangements of X defined universally, i.e., independently of the coefficients \(a_ n\).
reviewed by: Ferenc Móricz
Mathematics Subject Classification ID: 30B40
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4093823
zbMATH Keywords: random power series
MaRDI profile type: Publication
cites work: Q3276774
cites work: Q5587572
cites work: On divergence and absolute convergence of series arising from strongly multiplicative orthogonal functions
cites work: Q4089282
cites work: D. Blackwell's conjecture on power series with random coefficients
cites work: Moment multipliers for power series
description: scientific article; zbMATH DE number 4093823