  We study stochastic evolution equations describing the dynamics of open
quantum systems. First, using resolvent approximations, we obtain a sufficient
condition for regularity of solutions to linear stochastic Schroedinger
equations driven by cylindrical Brownian motions applying to many physical
systems. Then, we establish well-posedness and norm conservation property of a
wide class of open quantum systems described in position representation.
Moreover, we prove Ehrenfest-type theorems that describe the evolution of the
mean value of quantum observables in open systems. Finally, we give a new
criterion for existence and uniqueness of weak solutions to non-linear
stochastic Schroedinger equations. We apply our results to physical systems
such as fluctuating ion traps and quantum measurement processes of position.
