We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe (2000). Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed. Short title: A New Maximal Inequality I Results Let (Xi)i∈Z be a...
