Large Deviations for Gaussian Stationary Processes and Semi-Classical Analysis

被引：1
|
作者：
Bercu, Bernard [1 ]
Bony, Jean-Francois [1 ]
Bruneau, Vincent [1 ]
机构：
[1] Univ Bordeaux 1, Inst Math Bordeaux, UMR CNRS 5251, F-33405 Talence, France
来源：
SEMINAIRE DE PROBABILITES XLIV | 2012年 / 2046卷
关键词：
Large deviations; Gaussian processes; Distribution of eigenvalues; Toeplitz matrices;
D O I：
10.1007/978-3-642-27461-9_19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：409 / 428
页数：20
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