We present a direct derivation of the theorem of M. Maxwell and M. Woodroofe (Ann. Probab. vol. 28 (2000) 713-724), on martingale approximation of additive functionals of stationary Markov processes, from the non-reversible version of the Kipnis-Varadhan theorem.
"Comment on a theorem of M. Maxwell and M. Woodroofe." Electron. Commun. Probab. 18 1 - 4, 2013. https://doi.org/10.1214/ECP.v18-2366