CENTRAL LIMIT THEOREMS FOR ADDITIVE FUNCTIONALS OF MARKOV CHAINS1 By Michael Maxwell and Michael Woodroofe

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 X1 2 <∞. 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.