On large deviations for some sequences of weighted means of Gaussian processes

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• 作者：Rita Giuliano^a ; ^{giuliano@dm.unipi.it" class="auth_mail} ; Claudio Macci^b ; ^{macci@mat.uniroma2.it" class="auth_mail} ; Barbara Pacchiarotti^b ; ^{pacchiar@mat.uniroma2.it" class="auth_mail}
• 关键词：Almost sure central limit theorem ; Covariance function ; Hellinger distance ; Relative entropy
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 June, 2014
• 年：2014
• 卷：414
• 期：2
• 页码：612-631
• 全文大小：378 K

文摘

In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature.