Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes

Abstract

We extend the forward-backward martingale decomposition of Meyer-Zheng-Lyons's type from the symmetric case to the general stationary situation for the partial sum S.(ƒ) with ƒ satisfying a finite energy condition. As corollaries we obtain easily a maximal inequality and a tightness result related to Donsker's invariance principle, and especially a criterion of a.s. compactness related to Strassen's strong invariance principle.