Appears in collection : 2018 - T2 - WS1 - Observability and estimation in quantum dynamics

Quantum trajectories are Markov processes with singular transition which prevent to use usual Markov Theorems in order to study their large time behaviour. Their large time behaviour is linked with the notion of invariant measure (stationary regime). The question of existence and uniqueness of teh invariant measure is a tedious question. With Tristan Benoist, Martin Frass and Yan Pautrat we solve this problem by using product of random matrices techniques. In this talk I shall present these results.