On bilinear forms in Gaussian random variables and Toeplitz matrices (Q1105276)

Let \(B_ n=\sum^{n}_{i,j=1}a_{i-j}X_ iX_ j\) be a bilinear form, where \(X_ i\) is a zero mean stationary Gaussian sequence. The results of \textit{U. Grenander} and \textit{G. Szegö}, Toeplitz forms and their applications. (1958; Zbl 0080.095), on the asymptotic behaviour of \(B_ n\) are improved. The improved result on the asymptotic behaviour of the trace of products of Toeplitz matrices is used for this purpose.