  The set of continuous norm-preserving stochastic Schrodinger equations
associated with the Lindblad master equation is introduced. This set is used to
describe the localization properties of the state vector toward eigenstates of
the environment operator. Particular focus is placed on determining the
stochastic equation which exhibits the highest rate of localization for wide
open systems. An equation having such a property is proposed in the case of a
single non-hermitian environment operator. This result is relevant to numerical
simulations of quantum trajectories where localization properties are used to
reduce the number of basis states needed to represent the system state, and
thereby increase the speed of calculation.
