Uniform CLT for Markov chains with a countable state space

Taiwanese Journal of Mathematics

Volumn 1, Issue 4, 1997, Pages 481-498

  Tsai, Tsung Hsi ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Empirical process; Markov chain; Regenerative process; Uniform CLT

Indexed keywords

EID: 0012902468     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500406124     Document Type: Article

References (16)

1. K. L. Chung, Markov Chain with Stationary Probability, Springer, 1967.
2. Yu. A. Davydov, Mixing conditions for Markov chains, Theory Probab. Appl. 28 (1973), 313-318.
3. S. A. Dhompongsa, Note on the almost sure approximation of empirical prosess of weakly dependent random vectors, Yokohama Math. J. 32 (1984), 113-121.
4. P. Doukhan, P. Massart, and E. Rio, Invariance principles for absolutely regular empirical processes, Ann. Inst. H. Poincaré Probab. Statist. 31, no. 2 (1995), 393-427.
5. R. M. Dudley, A Course on Empirical Processes, Lecture Notes in Math, Vol. 1097, Spring, New York, 1984.
6. R. Durrett, Probability: Theory and Examples, Wadsworth & Brooks/Cole Statistics/Probability Series, 1991.
7. M. Durst, and R. M. Dudley, Empirical processes, Vapnik-Cervonenkis classes and Poisson processes, Probab. Math. Statist. 1 (1981), 109-115.
8. E. Giné and J. Zinn, Lectures on the central limit theorem for empirical processes, Lect. Notes in Math. Vol. 1221, 1986, pp. 50-113.
9. B. V. Gnedenko and A. K. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, 1967.
10. M. Ledoux and M. Talagrad, Probability in Banach spaces, Springer-Verlag, 1991.
11. S. Levental, Uniform limit theorems for Harris recurrent Markov chains, Probab. Theory Related Fields 80 (1988), 101-118.
12. S. Levental, Uniform CLT for Markov chain with a countable state space, Stochastic Process. Appl. 34 (1990), 245-253.
13. P. Massart, Invariance principles for empirical processes: the weakly case, Quelques problèmes de vitesse de convergence pour des measures empiriques, Thèse d'Etat, Université de Paris-Sud, 1987.
14. 2-bracketing, Ann. Probab. 15 (1987), 897-919.
15. Pollard, D. Convergence of Stochastic Processes, Springer, New York, 1984.
16. S. M. Ross, Stochastic Processes, New York, Wiley, 1983.