Abstract
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 first author. An alternative proof of the needed result on Toeplitz matrices, based on semi-classical analysis, is also provided.
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Acknowledgements
The authors would like to thanks A. Böttcher for providing the reference of Roch and Silbermann. They also thank the anonymous referee for his careful reading of the paper.
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Bercu, B., Bony, JF., Bruneau, V. (2012). Large Deviations for Gaussian Stationary Processes and Semi-Classical Analysis. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_19
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DOI: https://doi.org/10.1007/978-3-642-27461-9_19
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