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

Abstract : In this paper we study the moderate deviation principle for linear statistics of the type S (n) =a (iaZ) c (n,i) xi (i) , where c (n,i) are real numbers, and the variables xi (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.
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Submitted on : Tuesday, May 1, 2012 - 7:37:20 PM
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Florence Merlevede, Magda Peligrad. Moderate Deviations for Linear Processes Generated by Martingale-Like Random Variables. Journal of Theoretical Probability, Springer, 2010, 23 (1), pp.277--300. ⟨10.1007/s10959-009-0218-6⟩. ⟨hal-00693028⟩

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