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.
Citation
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