A central limit theorem for functions of a Markov chain with applications to shifts

Michael Woodroofe

Stochastic Processes and their Applications, 1992, vol. 41, issue 1, 33-44

Abstract: A sufficient condition is developed for partial sums of a function of a stationary, ergodic Markov chain to be asymptotically normal. For Bernoulli and Lebesgue shifts, the condition may be related to the Fourier coefficients of the given function; and the latter condition is shown to be satisfied by most square integrable functions in the case of Bernoulli shifts.

Date: 1992
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