The central limit theorem for Markov chains started at a point

Probability Theory and Related Fields

Volumn 125, Issue 1, 2003, Pages 73-76

  Derriennic, Yves ^a   Lin, Michael ^b  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037934608     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400200215     Document Type: Article

References (9)

1. [DL1] Derriennic, Y., Lin, M.: Sur le théorème limite central de Kipnis et Varadhan pour les chaînes réversibles ou normales, C. R. Acad. Sciences Paris Série 1323, 1053-1057 (1996)
2. [DL2] Derriennic, Y., Lin, M.: Fractional Poisson equations and ergodic theorems for fractional coboundaries, Israel J. Math. 123, 93-130 (2001)
3. [DL3] Derriennic, Y, Lin, M.: The central limit theorem for Markov chains with normal transitions, started at a point, Probab. Theory Relat. Fields 119, 508-528 (2001)
4. [F] Feller, W.: An introduction to probability theory and its applications, Vol II, 2nd ed., Wiley, New York, 1971
5. [GL1] Gordin, M., Lifshitz, B.: A central limit theorem for Markov processes, Soviet Math. Doklady 19, 392-394 (1978)
6. [GL2] Gordin, M., Lifshitz, B.: The central limit theorem for Markov processes with normal transition operator, and a strong form of the central limit theorem, §§IV.7 and IV.8 in A. Borodin and I. Ibragimov, limit theorem for functionals of random walks, Proc. Steklov Inst. Math. 195 (1994); English translation Amer. Math. Soc. 1995
7. [KV] Kipnis, C., Varadhan, S.R.: Central limit theorems for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys. 104, 1-19 (1986)
8. [MW] Maxwell, M., Woodroofe, M.: Central limit theorems for additive functionals of Markov chains, Ann. Probab. 28, 713-724 (2000)
9. [Z] Zygmund, A.: Trigonometric series, Vol. I, corrected 2nd, ed., Cambridge University Press, Cambridge, 1968