Bilinear Forms in Gaussian Random Variables, Toeplitz Matrices and Parseval's Relation

摘要

A result of Szego is approved on the asympototic behaviour of the trace of products of Toeplitz matrices. As an application, this result is improved on the limiting behavior of the bilinear forms sum of (a sub(i-j) X sub i X sub j) from ij = l to n where X sub i, is a stationary Gaussian sequence. A large deviations result is derived as well.