  A characterization of the unbounded stochastic generators of quantum
completely positive flows is given. This suggests the general form of quantum
stochastic adapted evolutions with respect to the Wiener (diffusion), Poisson
(jumps), or general Quantum Noise. The corresponding irreversible Heisenberg
evolution in terms of stochastic completely positive (CP) maps is constructed.
The general form and the dilation of the stochastic completely dissipative (CD)
equation over the algebra L(H) is discovered, as well as the unitary quantum
stochastic dilation of the subfiltering and contractive flows with unbounded
generators. A unitary quantum stochastic cocycle, dilating the subfiltering CP
flows over L(H), is reconstructed.
