Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
Djellout, H. ; Guillin, A. ; Wu, L.
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006), p. 393-416 / Harvested from Numdam
@article{AIHPB_2006__42_4_393_0,
     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},
     volume = {42},
     year = {2006},
     pages = {393-416},
     doi = {10.1016/j.anihpb.2005.04.006},
     mrnumber = {2242954},
     zbl = {1100.60010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2006__42_4_393_0}
}
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) pp. 393-416. doi : 10.1016/j.anihpb.2005.04.006. http://gdmltest.u-ga.fr/item/AIHPB_2006__42_4_393_0/

[1] F. Avram, On bilinear forms in Gaussian random variables and Toeplitz matrices, Probab. Theory Related Fields 79 (1988) 37-45. | MR 952991 | Zbl 0648.60043

[2] B. Bercu, F. Gamboa, A. Rouault, Large deviations for quadratic forms of Gaussian stationary processes, Stochastic Process. Appl. 71 (1997) 75-90. | MR 1480640 | Zbl 0941.60050

[3] S. Bobkov, F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 163 (1999) 1-28. | MR 1682772 | Zbl 0924.46027

[4] P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, Springer-Verlag, New York, 1991. | MR 1093459 | Zbl 0604.62083

[5] W. Bryc, A. Dembo, On large deviations of empirical measures for stationary Gaussian processes, Stochastic Process. Appl. 58 (1995) 23-34. | MR 1341552 | Zbl 0833.60027

[6] W. Bryc, A. Dembo, Large deviations for quadratic functionals of Gaussian functionals, J. Theoret. Probab. 10 (1997) 307-332. | MR 1455147 | Zbl 0894.60026

[7] R.M. Burton, H. Dehling, Large deviations for some weakly dependent random processes, Statist. Probab. Lett. 9 (1990) 397-401. | MR 1060081 | Zbl 0699.60016

[8] P.L. Butzer, R.J. Nessel, Fourier Analysis and Approximation, vol. I, Birkhäuser, 1971. | MR 510857 | Zbl 0217.42603

[9] X. Chen, Moderate deviations for m-dependent random variables with Banach space values, Statist. Probab. Lett. 35 (1997) 123-134. | MR 1483265 | Zbl 0887.60010

[10] A. Dembo, O. Zeitouni, Large Deviations Techniques and their Applications, Jones and Bartlett, Boston, MA, 1993. | MR 1202429 | Zbl 0793.60030

[11] J.D. Deuschel, D.W. Stroock, Large Deviations, Academic Press, Boston, 1989. | MR 997938 | Zbl 0705.60029

[12] H. Djellout, A. Guillin, Large deviations and moderate deviations for moving average processes, Ann. Math. Fac. Toulouse 10 (2001) 23-31. | Numdam | MR 1928987 | Zbl 1002.60028

[13] H. Djellout, A. Guillin, L. Wu, Transportation cost-information inequalities for random dynamical systems and diffusions, Ann. Probab. 32 (2004) 2702-2732. | MR 2078555 | Zbl 1061.60011

[14] M.D. Donsker, S.R.S. Varadhan, Large deviations for stationary Gaussian processes, Commun. Math. Phys. 97 (1985) 187-210. | MR 782966 | Zbl 0646.60030

[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 871252 | Zbl 0586.60019

[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 1061950 | Zbl 0717.62015

[17] P. Hall, C.C. Heyde, Martingale Limit Theory and its Application, Academic Press, New York, 1980. | MR 624435 | Zbl 0462.60045

[18] T. Jiang, M.B. Rao, X. Wang, Moderate deviations for some weakly dependent random processes, Statist. Probab. Lett. 15 (1992) 71-76. | MR 1190249 | Zbl 0761.60023

[19] T. Jiang, M.B. Rao, X. Wang, Large deviations for moving average processes, Stochastic Process. Appl. 59 (1995) 309-320. | MR 1357658 | Zbl 0836.60025

[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 1767995 | Zbl 0957.60016

[21] M. Rosenblatt, Gaussian and Non-Gaussian Linear Time Series and Random Fields, Springer-Verlag, New York, 2000. | MR 1742357 | Zbl 0933.62082

[22] G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, New York, 1994. | MR 1280932 | Zbl 0925.60027

[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 2189197