Central limit theorems for additive functionals of Markov chains

摘要

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S-n = g(X-1) + ... + g(X-n), where E[g(X-1)] = 0 and E[g(X-1)(2)] < . The conditions imposed restrict the moments of g and the growth of the conditional means E(S-nX-1). 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. [References: 12]