  We address the question of stability of quantum trajectories, also referred
as quantum filters}. We determine the limit of the quantum fidelity between the
true quantum trajectory and the {estimated one}. Under a purification
assumption we show that this limit equals to one meaning that quantum filters
are stable. In the general case, under an identifiability and a spectral
assumption we show that the limit of the Cesaro mean of the estimated
trajectory is the same as the true one.
