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August, 1979 The Almost Sure Stability of Quadratic Forms
James M. Wilmesmeier, F. T. Wright
Ann. Probab. 7(4): 738-743 (August, 1979). DOI: 10.1214/aop/1176994995

Abstract

Let $w_{jk}$ be a doubly indexed sequence of weights, let $\{X_k\}$ be a sequence of independent random variables and let $Q_n = \Sigma^n_{j,k=1} w_{jk}X_jX_k$. Sufficient conditions for the almost sure stability of $Q_n$ are given and the "tightness" of these conditions is investigated. These quadratic forms are weighted sums of dependent variables; however, their stability properties are very much like those established in the literature for weighted sums of independent variables.

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James M. Wilmesmeier. F. T. Wright. "The Almost Sure Stability of Quadratic Forms." Ann. Probab. 7 (4) 738 - 743, August, 1979. https://doi.org/10.1214/aop/1176994995

Information

Published: August, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0411.60033
MathSciNet: MR537219
Digital Object Identifier: 10.1214/aop/1176994995

Subjects:
Primary: 60F15
Secondary: 60G50

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 4 • August, 1979
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