Abstract
In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.
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Supported in part by a Charles Phelps Taft Memorial Fund grant, NSF DMS-0830579 and NSA grants H98230-09-1-0005 and H98230-11-1-0135.
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Peligrad, M. Central limit theorem for triangular arrays of non-homogeneous Markov chains. Probab. Theory Relat. Fields 154, 409–428 (2012). https://doi.org/10.1007/s00440-011-0371-6
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DOI: https://doi.org/10.1007/s00440-011-0371-6
Keywords
- Central limit theorem
- Triangular arrays
- Non-homogeneous Markov chains
- Maximal coefficient of correlation
Mathematics Subject Classification (2000)
- Primary 60F05
- 60J10
- 60G48