ON STOCHASTIC GENERATORS OF COMPLETELY POSITIVE COCYCLES

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.