On the interpolation property and dominated decomposition property of quasimartingales

For a quasimartingale majorized by another quasimartingale, it is natural to ask whether a third quasimartingale can be inserted between them. In this paper, we give an affirmative answer to this problem. We also establish a dominated decomposition property of quasimartingales. In addition, we show that a weak interpolation property holds for supermartingales and local supermartingales. Our approach also yields the interpolation property and dominated decomposition property for Markov chains.