Large deviations for Gaussian stationary processes and semi-classical analysis

Bernard Bercu (1, 2) , Jean-François Bony (2) , Vincent Bruneau (2)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux

In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary processes. It is established by the conjunction of a result of Roch and Silbermann on the spectrum of products of Toeplitz matrices together with the analysis of large deviations carried out by Gamboa, Rouault and the rst author. An alternative proof of the needed result on Toeplitz matrices, based on semi-classical analysis, is also provided.

Domaines: Probabilités [math.PR]

Bernard Bercu, Jean-François Bony, Vincent Bruneau. Large deviations for Gaussian stationary processes and semi-classical analysis. Séminaire de Probabilités, 2012, 44, pp.409-428. ⟨10.1007/978-3-642-27461-9⟩. ⟨hal-00642658⟩