no. 4
Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 4, pp. 393-416. 
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     author = {Djellout, H. and Guillin, A. and Wu, L.},
     title = {Moderate deviations of empirical periodogram and non-linear functionals of moving average processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {393--416},
     publisher = {Elsevier},
     volume = {42},
     number = {4},
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     doi = {10.1016/j.anihpb.2005.04.006},
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     zbl = {1100.60010},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2005.04.006/}
}
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Djellout, H.; Guillin, A.; Wu, L. Moderate deviations of empirical periodogram and non-linear functionals of moving average processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 4, pp. 393-416. doi : 10.1016/j.anihpb.2005.04.006. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.04.006/

[1] F. Avram, On bilinear forms in Gaussian random variables and Toeplitz matrices, Probab. Theory Related Fields 79 (1988) 37-45. | MR | Zbl

[2] B. Bercu, F. Gamboa, A. Rouault, Large deviations for quadratic forms of Gaussian stationary processes, Stochastic Process. Appl. 71 (1997) 75-90. | MR | Zbl

[3] S. Bobkov, F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 163 (1999) 1-28. | MR | Zbl

[4] P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, Springer-Verlag, New York, 1991. | MR | Zbl

[5] W. Bryc, A. Dembo, On large deviations of empirical measures for stationary Gaussian processes, Stochastic Process. Appl. 58 (1995) 23-34. | MR | Zbl

[6] W. Bryc, A. Dembo, Large deviations for quadratic functionals of Gaussian functionals, J. Theoret. Probab. 10 (1997) 307-332. | MR | Zbl

[7] R.M. Burton, H. Dehling, Large deviations for some weakly dependent random processes, Statist. Probab. Lett. 9 (1990) 397-401. | MR | Zbl

[8] P.L. Butzer, R.J. Nessel, Fourier Analysis and Approximation, vol. I, Birkhäuser, 1971. | MR | Zbl

[9] X. Chen, Moderate deviations for m-dependent random variables with Banach space values, Statist. Probab. Lett. 35 (1997) 123-134. | MR | Zbl

[10] A. Dembo, O. Zeitouni, Large Deviations Techniques and their Applications, Jones and Bartlett, Boston, MA, 1993. | MR | Zbl

[11] J.D. Deuschel, D.W. Stroock, Large Deviations, Academic Press, Boston, 1989. | MR | Zbl

[12] H. Djellout, A. Guillin, Large deviations and moderate deviations for moving average processes, Ann. Math. Fac. Toulouse 10 (2001) 23-31. | Numdam | MR | Zbl

[13] H. Djellout, A. Guillin, L. Wu, Transportation cost-information inequalities for random dynamical systems and diffusions, Ann. Probab. 32 (2004) 2702-2732. | MR | Zbl

[14] M.D. Donsker, S.R.S. Varadhan, Large deviations for stationary Gaussian processes, Commun. Math. Phys. 97 (1985) 187-210. | MR | Zbl

[15] R. Fox, M. Taqqu, Central limit theorems for quadratic forms in random variables having long-range dependence, Probab. Theory Related Fields 74 (1987) 213-240. | MR | Zbl

[16] L. Giraitis, D. Surgailis, A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate, Probab. Theory Related Fields 86 (1990) 87-104. | MR | Zbl

[17] P. Hall, C.C. Heyde, Martingale Limit Theory and its Application, Academic Press, New York, 1980. | MR | Zbl

[18] T. Jiang, M.B. Rao, X. Wang, Moderate deviations for some weakly dependent random processes, Statist. Probab. Lett. 15 (1992) 71-76. | MR | Zbl

[19] T. Jiang, M.B. Rao, X. Wang, Large deviations for moving average processes, Stochastic Process. Appl. 59 (1995) 309-320. | MR | Zbl

[20] M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, in: Séminaire de probabilités XXXIII, Lecture Notes in Math., vol. 1709, Springer, 1999, pp. 120-216. | Numdam | MR | Zbl

[21] M. Rosenblatt, Gaussian and Non-Gaussian Linear Time Series and Random Fields, Springer-Verlag, New York, 2000. | MR | Zbl

[22] G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, New York, 1994. | MR | Zbl

[23] L. Wu, An introduction to large deviations, in: Yan J.A., Peng S., Fang S., Wu L. (Eds.), Several Topics in Stochastic Analysis, Academic Press of China, Beijing, 1997, pp. 225-336, (in Chinese).

[24] L. Wu, On large deviations for moving average processes, in: Lai T.L., Yang H.L., Yung S.P. (Eds.), Probability, Finance and Insurance, Proceeding of a Workshop at the University of Hong-Kong, 15-17 July 2002, World Scientific, Singapore, 2004, pp. 15-49. | MR

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