  When measuring a complex quantum system, we are often interested in only a
few degrees of freedom-the plant, while the rest of them are collected as
auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and
simply ignoring its dynamics, i.e., adiabatically eliminating it, will prevent
us from predicting the true quantum behavior of the plant. We generalize the
technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and
develop a formalism that allows us to eliminate the bath non-adiabatically in
continuous quantum measurements, and obtain a non-Markovian stochastic master
equation for the plant which we focus on. We apply this formalism to three
interesting examples relevant to current experiments.
