  A quantum system S undergoing continuous time measurement is usually
described by a jump-diffusion stochastic differential equation. Such an
equation is called a stochastic master equation and its solution is called a
quantum trajectory. This solution describes actually the evolution of the state
of S. In the context of Quantum Non Demolition measurement, we investigate the
large time behavior of this solution. It is rigorously shown that, for large
time, this solution behaves as if a direct Von Neumann measurement has been
performed at time 0. In particular the solution converges to a random pure
state which is related to the wave packet reduction postulate. Using theory of
Girsanov transformation, we determine precisely the exponential rate of
convergence towards this random state. The important problem of state
estimation (used in experiment) is also investigated.
