On the pointwise central limit theorem and mixtures of stable distributions

Statistics and Probability Letters

Volumn 29, Issue 4, 1996, Pages 361-368

  Berkes, I ^a   Csaki E ^a  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

Author keywords

Mixtures; Pointwise central limit theorem; Stable distributions

Indexed keywords

EID: 0030590336     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-7152(95)00192-1     Document Type: Article

References (11)

1. De Acosta, A. and E. Giné (1979), Convergence of moments and related functional in the general central limit theorem in Banach spaces, Z. Wahrsch. Verw. Gebiete 48, 213-231.
2. Berkes, I. (1995), On the almost sure central limit theorem and domains of attraction, Probab. Theory Related Fields 102, 1-18.
3. Berkes, I. and H. Dehling (1993), Some limit theorems in log density, Ann. Probab. 21, 1640-1670.
4. Berkes, I. and H. Dehling (1994), On the almost sure central limit theorem for random variables with infinite variance, J. Theoret. Probab. 7, 667-680.
5. Brosamler, G. (1988), An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104, 561-574.
6. Feller, W. (1966), An Introduction to Probability Theory and its Applications, Vol. II (Wiley, New York).
7. Fisher, A, (1989), A pathwise central limit theorem for random walks, preprint.
8. Kelker, D. (1971), Infinite divisibility and variance mixtures of the normal distribution, Ann. Math. Statist. 42, 802-808.
9. Lacey, M. and W. Philipp (1990), A note on the almost everywhere central limit theorem, Statist. Probab. Lett. 9, 201-205.
10. Peligrad, M. and P. Révész (1991), On the almost sure central limit theorem, in: A. Bellow and R. Jones, eds., Almost everywhere convergence II (Academic Press, New York) pp. 209-225.
11. Schatte, P. (1988), On strong versions of the central limit theorem, Math. Nachr. 137, 249-256.