A characterization of the generators of quantum stochastic cocycles of
completely positive (CP) maps Is given in terms of the complete dissi
pativity (CD) of Its form-generator. The pseudo-Hilbert dilation of th
e stochastic form-generator and the pre-Hilbert dilation of the corres
ponding dissipator are Found. The general form of the linear continuou
s structural maps for the algebra of all bounded operators is derived
and the quantum stochastic Row for the corresponding cocycle is outlin
ed. It is proved that any w-analytical bounded CD form-generator give
s rise to a quantum stochastic CP cocycle over a von Neumann algebra.