Abstract
We obtain sufficient conditions that should be imposed on a functionf in order that, for ergodic Markov chains, the sum
be asymptotically normal.
References
N. V. Moskal'tsova and V. M. Shurenkov, “On potentials of ergodic Markov chains,”Ukr. Mat. Zh.,46, No. 4, 446–449 (1994).
N. V. Moskal'tsova and V. M. Shurenkov, “Central limit theorem for special classes of functions in ergodic chains,”Ukr. Mat. Zh.,46, No. 8, 1092–1094 (1994).
V. M. Shurenkov,Ergodic Markov Processes [in Russian], Nauka, Moscow (1989).
E. Nummelin,General Irreducible Markov Chains and Nonnegative Operators, Cambridge University Press, Cambridge (1984).
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Deceased.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 118–120, January, 1995.
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Moskal'tsova, N.V., Shurenkov, V.M. Remark on the central limit theorem for ergodic chains. Ukr Math J 47, 138–141 (1995). https://doi.org/10.1007/BF01058805
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DOI: https://doi.org/10.1007/BF01058805