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Sample Path Large Deviations for Squares of Stationary Gaussian Processes

Abstract : In this paper, we show large deviations for random step functions of type Zn(t) = 1 n X[nt] k=1 X2 k ; where fXkgk is a stationary Gaussian process. We deal with the associated random measures n = 1 n Pn k=1 X2 k k=n. The proofs require a Szego theorem for generalized Toeplitz matrices, which is presented in the Appendix and is analogous to a result of Kac, Murdoch and Szego [10]. We also study the polygonal line built on Zn(t) and show moderate deviations for both random families.
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Contributor : Marguerite Zani <>
Submitted on : Sunday, March 3, 2013 - 11:36:13 AM
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Marguerite Zani. Sample Path Large Deviations for Squares of Stationary Gaussian Processes. Theory of Probability and Its Applications c/c of Teoriia Veroiatnostei i Ee Primenenie, Society for Industrial and Applied Mathematics, 2012, 57 (2), pp.395--405. ⟨hal-00796318⟩

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