Moment inequalities for sums of dependent random variables under projective conditions

Journal of Theoretical Probability

Volumn 22, Issue 1, 2009, Pages 146-163

  Rio, Emmanuel ^a  

^a UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

Author keywords

Martingale; Moment inequality; Projective criteria; Rosenthal inequality; Stationary sequences

Indexed keywords

EID: 58549102501     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-008-0155-9     Document Type: Article

References (18)

1. R.C. Bradley 1997 On quantiles and the central limit question for strongly mixing sequences J. Theor. Probab. 10 507 555
2. J. Bretagnolle C. Huber 1979 Estimation des densités: risque minimax Z. Wahrscheinlichkeitstheor. Verw. Geb. 47 119 137
3. D.L. Burkholder 1973 Distribution function inequalities for martingales Ann. Probab. 1 19 42
4. D.L. Burkholder 1988 Sharp inequalities for martingales and stochastic integrals Astérisque 157-158 75 94
5. X. Chen A. Guillin 2004 The functional moderate deviations for Harris recurrent Markov chains and applications Ann. Inst. Henri Poincaré Probab. Stat. 40 89 124
6. P. Doukhan F. Portal 1983 Moments de variables aléatoires mélangeantes C.R. Acad. Sci. Paris Sér. 1 297 129 132
7. P. Doukhan P. Massart E. Rio 1994 The functional central limit theorem for strongly mixing processes Ann. Inst. Henri Poincaré Probab. Stat. 30 63 82
8. T. Figiel P. Hitczenko W.B. Johnson G. Schechtman J. Zinn 1997 Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities Trans. Am. Math. Soc. 349 3 997 1027
9. E. Lesigne D. Volný 2001 Large deviations for martingales Stoch. Process. Their. Appl. 96 143 159
10. S.V. Nagaev 2007 On probability and moment inequalities for supermartingales and martingales Acta Appl. Math. 97 151 162
11. Nummelin, E.: General Irreducible Markov Chains and non Negative Operators. Cambridge University Press, Cambridge (1984)
12. M. Peligrad S. Utev 2005 A new maximal inequality and invariance principle for stationary sequences Ann. Probab. 33 2 798 815
13. p-inequality for stationary sequences and its applications Proc. Am. Math. Soc. 135 541 550
14. Y.F. Ren H.Y. Liang 2001 On the best constant in Marcinkiewicz-Zygmund inequality Stat. Probab. Lett. 53 3 227 233
15. Rio, E.: Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants. Mathématiques et Applications, vol. 31. Springer, Berlin (2000)
16. G. Viennet 1997 Inequalities for absolutely regular sequences: application to density estimation Probab. Theory. Relat. Fields 107 467 492
17. P. Whittle 1960 Bounds for the moments of linear and quadratic forms of independent random variables Teor. Veroyatn. ee Primen. 5 3 331 334
18. Wu, W.B., Zhao, Z.: Moderate deviations for stationary processes. Tech. Report, University of Chicago (2006). To appear in Stat. Sin.