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On large deviations for some sequences of weighted means of Gaussian processes |
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| Authors: | Rita Giuliano Claudio Macci Barbara Pacchiarotti |
| Institution: | 1. Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy;2. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy |
| Abstract: | 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. |
| Keywords: | Almost sure central limit theorem Covariance function Hellinger distance Relative entropy |
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