Abstract
 
Quantum trajectories of systems subjected to continuous monitoring exhibit particular stochastic behaviors such as "progressive collapses" and/or  ‘"quantum jumps", observed in various experiments, but also more peculiar features, ‘’quantum spikes’’  which may be viewed as aborted jumps. This lecture will aim at describing some statistical properties of quantum trajectories.  We shall discuss statistical aspects of progressive non-demolition weak measurements, as implemented in cavity QED for instance. We shall present a quantitative understanding of the statistics of quantum spikes and of their potential universality (in the sense that they are independent of the dynamical processes which generate them). As an illustration, we shall discuss a scheme to control quantum flux through back-action measurement providing a potential example of a mesoscopic Maxwell daemon.