Abstract
The aim of this paper is to prove a central limit theorem and an invariance principle for an additive functional of an ergodic Markov chain on a general state space, with respect to the law of the chain started at a point. No irreducibility assumption nor mixing conditions are imposed; the only assumption bears on the growth of the L 2-norms of the ergodic sums for the function generating the additive functional, which must be with . The result holds almost surely with respect to the invariant probability of the chain.
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Received: 17 October 2001 / Revised version: 5 April 2002 / Published Online: 24 October 2002
Mathematics Subject Classification (2000): 60F05, 60J05
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Derriennic, Y., Lin, M. The central limit theorem for Markov chains started at a point. Probab Theory Relat Fields 125, 73–76 (2003). https://doi.org/10.1007/s004400200215
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DOI: https://doi.org/10.1007/s004400200215
Keywords
- Markov Chain
- Limit Theorem
- Central Limit
- Central Limit Theorem