  In this paper we study the asymptotic behavior of linear processes having as
innovations mean zero, square integrable functions of stationary reversible
Markov chains. In doing so we shall preserve the generality of coefficients
assuming only that they are square summable. In this way we include in our
study the long range dependence case. The only assumption imposed on the
innovations is the absolute summability of their covariances. Besides the
central limit theorem we also study the convergence to fractional Brownian
motion. The proofs are based on general results for linear processes with
stationary innovations that have interest in themselves.
