Décomposition atomique de martingales de la classe
In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.
We establish consistent estimators of jump positions and jump altitudes of a multi-level step function that is the best -approximation of a probability density function . If itself is a step-function the number of jumps may be unknown.