Central limit theorem for sampled sums of dependent random variables

 Access to full text

 Full (PDF)

 Access to full text

1. A.D. Barbour, R.M. Gerrard and G. Reinert, Iterates of expanding maps. Probab. Theory Relat. Fields116 (2000) 151–180.  
2. J.M. Bardet, P. Doukhan, G. Lang and N. Ragache, Dependent Linderberg central limit theorem and some applications. ESAIM: PS12 (2008) 154–172.  
3. H.C.P. Berbee, Random walks with stationary increments and renewal theory. Math. Centre Tracts 112, Amsterdam (1979).  
4. P. Collet, S. Martinez and B. Schmitt, Exponential inequalities for dynamical measures of expanding maps of the interval. Probab. Theory. Relat. Fields123 (2002) 301–322.  
5. C. Coulon-Prieur and P. Doukhan, A triangular CLT for weakly dependent sequences. Statist. Probab. Lett.47 (2000) 61–68.  
6. D. Dacunha-Castelle and M. Duflo, Problèmes à temps mobile. Deuxième édition. Masson (1993).  
7. J. Dedecker and C. Prieur, New dependence coefficients, Examples and applications to statistics. Probab. Theory Relat. Fields132 (2005) 203–236.  
8. J. Dedecker, P. Doukhan, G. Lang, J.R. Leon, S. Louhichi and C. Prieur, Weak dependence: With Examples and Applications. Lect. Notes in Stat.190. Springer, XIV (2007).  
9. C. Deniau, G. Oppenheim and M.C. Viano, Estimation de paramètre par échantillonnage aléatoire. (French. English summary) [Random sampling and parametric estimation]. C. R. Acad. Sci. Paris Sér. I Math.306 (1988) 565–568.  
10. P. Doukhan and S. Louhichi, A new weak dependence condition and applications to moment inequalities. Stochastic Process. Appl.84 (1999) 313–342.  
11. N. Guillotin-Plantard and D. Schneider, Limit theorems for sampled dynamical systems. Stoch. Dynamics3 (2003) 477–497.  
12. F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations. Math. Z.180 (1982) 119–140.  
13. I.A. Ibragimov, Some limit theorems for stationary processes. Theory Probab. Appl.7 (1962) 349–382.  
14. J.F.C. Kingman, The ergodic theory of subadditive stochastic processes. J. R. Statist. Soc. B30 (1968) 499–510.  
15. M. Lacey, On weak convergence in dynamical systems to self-similar processes with spectral representation. Trans. Amer. Math. Soc.328 (1991) 767–778.  
16. M. Lacey, K. Petersen, D. Rudolph and M. Wierdl, Random ergodic theorems with universally representative sequences. Ann. Inst. H. Poincaré Probab. Statist.30 (1994) 353–395.  
17. A. Lasota and J.A. Yorke, On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc.186 (1974) 481–488.  
18. F. Merlevède and M. Peligrad, On the coupling of dependent random variables and applications. Empirical process techniques for dependent data. Birkhäuser, Boston (2002), pp. 171–193.  
19. T. Morita, Local limit theorem and distribution of periodic orbits of Lasota-Yorke transformations with infinite Markov partition. J. Math. Soc. Jpn46 (1994) 309–343.  
20. M. Peligrad and S. Utev, Central limit theorem for linear processes. Ann. Probab.25 (1997) 443–456.  
21. E. Rio, About the Lindeberg method for strongly mixing sequences. ESAIM: PS1 (1995) 35–61.  
22. M. Rosenblatt, A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. USA 42 (1956) 43–47.  
23. Y.A. Rozanov and V.A. Volkonskii, Some limit theorems for random functions I. Theory Probab. Appl.4 (1959) 178–197.  
24. C.J. Stone, On local and ratio limit theorems. Proc. Fifth Berkeley Symp. Math. Statist. Probab. Univ. Californie (1966), pp. 217–224.  
25. S.A. Utev, Central limit theorem for dependent random variables. Probab. Theory Math. Statist.2 (1990) 519–528.  
26. S.A. Utev, Sums of random variables with $\varphi$-mixing. Siberian Adv. Math.1 (1991) 124–155.  
27. C.S. Withers, Central limit theorems for dependent variables. I. Z. Wahrsch. Verw. Gebiete57 (1981) 509–534 (corrigendum in Z. Wahrsch. Verw. Gebiete63 (1983) 555).  

1. Nadine Guillotin-Plantard, Clémentine Prieur, Limit theorem for random walk in weakly dependent random scenery