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"Quantum trajectories" are solutions of stochastic differential equations ofnon-usual type. Such equations are called "Belavkin" or "StochasticSchr\"odinger Equations" and describe random phenomena in continuousmeasurement theory of Open Quantum System. Many recent investigations deal withthe control theory in such model. In this article, stochastic models aremathematically and physically justified as limit of concrete discreteprocedures called "Quantum Repeated Measurements". In particular, this gives arigorous justification of the Poisson and diffusion approximation in quantummeasurement theory with control. Furthermore we investigate some examples usingcontrol in quantum mechanics.

Poisson and Diffusion Approximation of Stochastic Schrodinger equations with Control