Properties of Hida processes on 2. 1. N-Hida processes

If E is an ordered set, we study the processes Yt, t [set membership, variant] E, for which the vectorial spaces t generated by all the conditional expectations E(Ys[beta]t) for s >= t have finite dimensions d(t) <= N. (t is some convenient filtration.) We first develop a geometrical approach in the general situation and give a "Goursat's representation" Yt = [Sigma]fi(t)Mi(t), where the Mi(t) are martingales. We then restrict us to the cases E = or E = 2 and give representations of the processes by the mean of stochastic integrals of "Goursat's kernels." The special case when Yt is the solution of a differential equation is considered.