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.
Publié le : 1979-08-14
Classification:
Stability,
quadratic forms,
degenerate convergence,
almost sure convergence,
60F15,
60G50
@article{1176994995,
author = {Wilmesmeier, James M. and Wright, F. T.},
title = {The Almost Sure Stability of Quadratic Forms},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 738-743},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994995}
}
Wilmesmeier, James M.; Wright, F. T. The Almost Sure Stability of Quadratic Forms. Ann. Probab., Tome 7 (1979) no. 6, pp. 738-743. http://gdmltest.u-ga.fr/item/1176994995/