  We consider quantum stochastic processes and discuss a level 2.5 large
deviation formalism providing an explicit and complete characterisation of
fluctuations of time-averaged quantities, in the large-time limit. We analyse
two classes of quantum stochastic dynamics, within this framework. The first
class consists of the quantum jump trajectories related to photon detection;
the second is quantum state diffusion related to homodyne detection. For both
processes, we present the level 2.5 functional starting from the corresponding
quantum stochastic Schr\"odinger equation and we discuss connections of these
functionals to optimal control theory.
