  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.
