Under regularity assumptions, we establish a sharp largedeviation principle for Hermitian quadratic forms ofstationary Gaussian processes. Our result is similar tothe well-known Bahadur-Rao theorem [2] on the samplemean. We also provide several examples of applicationsuch as the sharp large deviation properties ofthe Neyman-Pearson likelihood ratio test, of the sum of squares,of the Yule-Walkerestimator of the parameter of a stable autoregressive Gaussian process,and finally of the empirical spectral repartition function.
