Abstract
In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.
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M. Peligrad is supported in part by a Charles Phelps Taft Memorial Fund grant, and NSA grants, H98230-07-1-0016 and H98230-09-1-0005. E. Rio is supported in part by Centre INRIA Bordeaux Sud-Ouest & Institut de Mathématiques de Bordeaux.
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Merlevède, F., Peligrad, M. & Rio, E. A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probab. Theory Relat. Fields 151, 435–474 (2011). https://doi.org/10.1007/s00440-010-0304-9
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DOI: https://doi.org/10.1007/s00440-010-0304-9
Keywords
- Deviation inequality
- Moderate deviations principle
- Semiexponential tails
- Weakly dependent sequences
- Strong mixing
- Absolute regularity
- Linear processes