Homogeneization of Markovian process and application to quantum continuous measurment

In many physical systems, we are faced with an interaction between mechanisms that evolve at very different time scales. In this seminar, we will consider Markovian processes with such characteristics, and we will exploit the time scale separation to obtain an effective Markovian dynamics on a reduced state space.
In particular, compared to existing studies, we will introduce a more general formalism. Finally, as a privileged example, we consider the limit of the strong continuous measure of quantum systems described by a Belavkin diffusive equation.