Abstract.
Let {X n } n ≥0 be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals of the form
where ƒ is a real π-centered function defined on E. Some similar results are also obtained for additive functionals which are martingales associated with {X n } n ≥0.
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Received: 15 September 1998 / Revised version: 1 April 1999
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Chen, X. On the limit laws of the second order for additive functionals of Harris recurrent Markov chains. Probab Theory Relat Fields 116, 89–123 (2000). https://doi.org/10.1007/PL00008724
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DOI: https://doi.org/10.1007/PL00008724
- Key words and phrases: Law of the iterated logarithm – Weak convergence – Harris recurrence – Regularity
- Mathematics Subject Classification (1991): 60F10, 60J10