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# Central Limit Theorems for Additive Functionals of Markov Chains

Michael Maxwell and Michael Woodroofe
The Annals of Probability
Vol. 28, No. 2 (Apr., 2000), pp. 713-724
Stable URL: http://www.jstor.org/stable/2652945
Page Count: 12
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## Abstract

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say Sn = g(X1) + ⋯ + g(Xn), where E[g(X1)] = 0 and $E[g(X_1)^2] < \infty$. The conditions imposed restrict the moments of g and the growth of the conditional means E(Sn∣ X1). No other restrictions on the dependence structure of the chain are required. When specialized to shift processes, the conditions are implied by simple integral tests involving g.

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