  In this work we propose a new approach for the numerical simulation of
kinetic equations through Monte Carlo schemes. We introduce a new technique
which permits to reduce the variance of particle methods through a matching
with a set of suitable macroscopic moment equations. In order to guarantee that
the moment equations provide the correct solutions, they are coupled to the
kinetic equation through a non equilibrium term. The basic idea, on which the
method relies, consists in guiding the particle positions and velocities
through moment equations so that the concurrent solution of the moment and
kinetic models furnishes the same macroscopic quantities.
