  We present the non-Markovian generalization of the widely used stochastic
Schrodinger equation. Our result allows to describe open quantum systems in
terms of stochastic state vectors rather than density operators, without
approximation. Moreover, it unifies two recent independent attempts towards a
stochastic description of non-Markovian open systems, based on path integrals
on the one hand and coherent states on the other. The latter approach utilizes
the analytical properties of coherent states and enables a microscopic
interpretation of the stochastic states. The alternative first approach is
based on the general description of open systems using path integrals as
originated by Feynman and Vernon.
