Moderate Deviations for Linear Processes Generated by Martingale-Like Random Variables

Florence Merlevède () and Magda Peligrad
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Florence Merlevède: Université Paris Est-Marne la Vallée, LAMA and C.N.R.S UMR 8050
Magda Peligrad: University of Cincinnati

Journal of Theoretical Probability, 2010, vol. 23, issue 1, 277-300

Abstract: Abstract In this paper we study the moderate deviation principle for linear statistics of the type S n =∑i∈Z c n,iξ i , where c n,i are real numbers, and the variables ξ i are in turn stationary martingale differences or dependent sequences satisfying projective criteria. As an application, we obtain the moderate deviation principle and its functional form for sums of a class of linear processes with dependent innovations that might exhibit long memory. A new notion of equivalence of the coefficients allows us to study the difficult case where the variance of S n behaves slower than n. The main tools are: a new type of martingale approximations and moment and maximal inequalities that are important in themselves.

Keywords: Moderate deviation; Functional moderate deviation principle; Linear processes; Martingale; Projection operator; 60F10; 60F17; 60G10; 60G42; 60M10 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0218-6

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