SAMPLE PATH LARGE DEVIATIONS FOR SQUARES OF STATIONARY GAUSSIAN PROCESSES

被引：3
作者：
Zani, M. [1 ]
机构：
[1] Univ Paris Est Creteil, CNRS, UMR 8050, Lab Anal & Math Appl, F-94010 Creteil, France
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2013年 / 57卷 / 02期
关键词：
Gaussian processes; large deviations; Szego theorem; Toeplitz matrices;
D O I：
10.1137/S0040585X97986023
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we show large deviations for random step functions of type Z(n)(t) = 1/n Sigma([nt])(k=1) X-k(2), where {X-k}(k) is a stationary Gaussian process. We deal with the associated random measures nu(n) = 1/n Sigma(n)(k=1) X-k(2)delta(k/n). The proofs require a Szego theorem for generalized Toeplitz matrices which is analogous to a result of Kac, Murdoch, and Szego [J. Rational Mech. Anal., 2 (1953), pp. 767-800]. We also study the polygonal line built on Zn(t) and show moderate deviations for both random families.
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收藏
页码：347 / U223
页数：11
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