  In this paper, we consider the special class of positive local submartingales
(X_{t}) of the form: X_{t}=N_{t}+A_{t}, where the measure (dA_{t}) is carried
by the set {t: X_{t}=0}. We show that many examples of stochastic processes
studied in the literature are in this class and propose a unified approach
based on martingale techniques to study them. In particular, we establish some
martingale characterizations for these processes and compute explicitly some
distributions involving the pair (X_{t},A_{t}). We also associate with X a
solution to the Skorokhod's stopping problem for probability measures on the
positive half-line.
