Abstract
The notion of (quantum) stochastic flow is introduced. The analysis of their infinitesimal generators leads to the introduction of the notion of stochastic derivation. The Lue non-abelian first cohomology space for stochastic derivations plays the analogue role of the first Hochshild cohomology group for usual derivations (i.e. it gives an idea of how large the space of inner (stochastic) derivations is with respect to the space of all derivations). We prove an addition theorem for stochastic derivations and an existence theorem for stochastic flows with bounded coefficients.
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