Moderate deviations for stationary sequences of Hilbert-valued bounded random variables |
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Authors: | Sophie Dede |
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Institution: | LPMA, UPMC Université Paris 6, Case courrier 188, 4, Place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | In this paper, we derive the Moderate Deviation Principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are martingale approximations and a new Hoeffding inequality for non-adapted sequences of Hilbert-valued random variables. Applications to Cramér-Von Mises statistics, functions of linear processes and stable Markov chains are given. |
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Keywords: | Hilbert space Moderate deviations Martingale approximation Stationary processes |
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