  This article provides a representation theorem for a set of Gaussian
processes; this theorem allows to build Gaussian processes with arbitrary
regularity and to write them as limit of random trigonometric series. We show
via Karhunen-Love theorem that this set is isometrically equivalent to l2. We
then prove that regularity of trajectory path of anyone of such processes can
be detected just by looking at decrease rate of l2 sequence associated to him
via isometry.
