Necessary and sufficient conditions for the conditional central limit theorem

Annals of Probability

Volumn 30, Issue 3, 2002, Pages 1044-1081

  Dedecker, Jérôme ^a   Merlevède, Florence ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Central limit theorem; Invariance principles; Stable convergence; Stationary processes; Triangular arrays

Indexed keywords

EID: 0036631350     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1029867121     Document Type: Article

References (34)

1. On mixing and stability of limit theorems
2. Critères d'ergodicité géométrique ou arithmétique de modèles linéaires perturbés à représentation markovienne
3. On quantiles and the central limit question for strongly mixing sequences
4. Limit theorems for functionals of ergodic Markov chains with general state space
5. Some examples and results in the theory of mixing and random-sum central limit theorems
6. On the functional central limit theorem for stationary processes
7. The functional central limit theorem for strongly mixing processes
8. Remarks on the CLT for weakly dependent random variables
9. On Gordin's central limit theorem for stationary processes
10. Some simple conditions for limit theorems to be mixing
11. On strong invariance principles under dependence assumptions
12. Limit laws for generalizations of martingales
13. The central limit theorem for stationary processes
14. On the central limit theorem for stationary processes
15. Some limit theorems for stationary processes
16. Minimal conditions in p-stable limit theorems
17. Dependant central limit theorems and invariance principles
18. A maximal inequality and dependent strong laws
19. Invariance principles for dependent variables
20. On the invariance principle for nonstationary mixingales
21. An invariance principle for dependent random variables
22. A note on two measures of dependence and mixing sequences
23. On stable sequences of events
24. Nonparametric estimators for time series
25. A central limit theorem and a strong mixing condition
26. Remarks on some nonparametric estimates of a density function
27. Contributions to central limit theory for dependent variables
28. Asymptotic distribution of sums of Rademacher functions
29. Two theorems on convergence in law for stochastic integrals and statistical applications
30. Subgeometric rates of convergence of f-ergodic Markov chains
31. Approximating martingales and the central limit theorem for strictly stationary processes