  Quantum trajectory techniques have been used in the theory of open systems as
a starting point for numerical computations and to describe the monitoring of a
quantum system in continuous time. Here we extend this technique and use it to
develop a general approach to the dynamics of quantum/classical hybrid systems.
By using two coupled stochastic differential equations, we can describe a
classical component and a quantum one which have their own intrinsic dynamics
and which interact with each other. A mathematically rigorous construction is
given, under the restriction of having a Markovian joint dynamics and of
involving only bounded operators on the Hilbert space of the quantum component.
An important feature is that, if the interaction allows for a flow of
information from the quantum component to the classical one, necessarily the
dynamics is dissipative. We show also how this theory is connected to a
suitable hybrid dynamical semigroup, which reduces to a quantum dynamical
semigroup in the purely quantum case and includes Liouville and
Kolmogorov-Fokker-Plank equations in the purely classical case. Moreover, this
semigroup allows to compare the proposed stochastic dynamics with various other
proposals based on hybrid master equations. Some simple examples are
constructed in order to show the variety of physical behaviours which can be
described; in particular, a model presenting hidden entanglement is introduced.
