Quantum stochastic differential equations of the form dkt = kt ◦ θαβ dLambdaβα(t) govern stochastic flows on a C∗-algebra A. We analyse this class of equation in which
the matrix of fundamental quantum stochastic integrators Lambda is infinite dimensional, and the coefficient matrix θ consists of bounded linear operators on A. Weak and strong forms of solution are distinguished, and a range of regularity conditions on the mapping matrix θ are
considered, for investigating existence and uniqueness of solutions. Necessary and sufficient conditions on θ are determined, for any sufficiently regular weak solution k to be completely positive. The further conditions on θ for k to also be a contraction process are found; and
when A is a von Neumann algebra and the components of θ are normal, these in turn imply sufficient regularity for the equation to have a strong solution. Weakly multiplicative and ∗-homomorphic solutions and their generators are also investigated. We then consider the right and left Hudson-Parthasarathy equations:
dXt = Fαβ Xt dLambdaβα(t), dYt = Yt Fαβ dLambdaβα(t), in which F is a matrix of bounded Hilbert space operators.Their solutions are interchanged by a time reversal operation on processes. The analysis of quantum stochastic flows is applied to obtain characterisations of the generators F of contraction, isometry and coisometry processes. In particular weak solutions that are contraction processes are shown to have bounded generators, and to be necessarily strong solutions.