A Uniform Estimate for the Rate of Convergence in the Multidimensional Central Limit Theorem for Homogeneous Markov Chains

International Journal of Mathematics and Mathematical Sciences

Volumn 19, Issue 3, 1996, Pages 441-450

  Gharib, M ^a  

^a QATAR UNIVERSITY   (Qatar)

Author keywords

Central limit theorem; homogeneous Markov chain; rate of convergence; Uniform estimate

Indexed keywords

EID: 18244372392     PISSN: 01611712     EISSN: 16870425     Source Type: Journal    
DOI: 10.1155/S0161171296000634     Document Type: Article

References (20)

1. Bhattacharya, R. N., Berry-Esseen bounds for the multidimensional central limit theorem, Bull. Amer. Math. Soc., 74 (1968), 285–287.
2. Bolthausen, E., The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains, Ζ Wahrscheinlichkeitstheorie und ver. Geb., 60, 3 (1982), 283–289.
3. Esseen, C. G., On the remainder term in the central limit theorem, Arkiv. Math., 8 1 (1969), 7–15.
4. Feller, W., On the Berry-Esseen theorem, Ζ. Wahrscheinlichkeits Theorie und ver. Geb., 3 (1968), 261–268.
5. Formanov, SH K, On the rate of convergence in the multidimensional limit theorem for homogeneous Markov chains, Dokl Akad. Nauk SSSR, 204 1 (1972), 29–31
6. Formanov, SH K, A uniform estimate in the multidimensional limit theorem for homogeneous Markov chains on the class of all convex measurable sets I., lzd-vo AN UzSSR, Phys.-Math. Ser., 3 (1972), 33–37
7. Formanov, SH K, A uniform estimate in the multidimensional limit theorem for homogeneous Markov chains on the class of all convex measurable sets II, lzd-vo AN UzSSR, Phys.-Math. Ser., 6 (1972), 35–42
8. Formanov, SH K, Some estimates of the rate of convergence in the multidimensional limit theorems for homogeneous Markov processes, Lecture Notes in Math., 550 (1976), 80–98
9. Formanov, SH K, On uniform estimates of the remainder term in the multidimensional limit theorem for homogeneous Markov chains I, lzd-vo AN UzSSR, Phys.-Math. Ser., 3 (1971), 24–30
10. Formanov, SH K, On uniform estimates of the remainder term in the multidimensional limit theorem for homogeneous Markov chains II, lzd-vo AN UzSSR, Phys.-Math. Ser., 5 (1971), 20–25
11. Ibragimov, I A and Osipov, L V., On an estimate of the remainder term in Lindeberg’s theorem, Theory Prob. Appl., 11 (1966), 125–128
12. Katz, M L., Note on the Berry-Esseen theorem, Ann. Math. Statist., 34 (1963), 1107–1108
13. Nagaev, S. V., Some limit theorems for stationary Markov chains, Theory Prob. Appl., 2 (1957), 378–406.
14. Nagaev, S. V., More exact statements of limit theorems for homogeneous Markov chains, Theory Prob. Appl., 6 (1961), 62–81.
15. Petrov, V. V. and Osipov, L. V., On estimates of the remainder term in the central limit theorem, Theory Prob. Appl., 12, 2 (1967), 322–329.
16. Petrov, V. V., Sums of Independent Random Variables, Springer-Verlag, 1975
17. Rotar, V. I., A non-uniform estimate for the rate of convergence in the multidimensional central limit theorem, Theory Prob. Appl., 15, 4 (1970), 630–648.
18. Sazonov, V. V., On the multidimensional central limit theorem, Sankhya, Ser. A, 30 (1968), 203–225.
19. Sirazhdinov, SKH. and Formanov, SH K., Limit theorems for sums of random vectors connected in a homogeneous Markov chain, Fan, Tashkent. (1979) (In Russian).
20. Vonbahr, B., Multidimensional integral limit theorem, Arkiv. Math., 7, 6 (1967), 71–88.