  We use the quantum kinetic theory to calculate the steady state and the
fluctuations of a trapped Bose-Einstein condensate at finite temperature. The
system is divided in a condensate and a non-condensate part. A quantum
mechanical description based on the number conserving Bogoliubov method is used
for describing the condensate part. The non-condensed particles are treated as
a classical gas in thermal equilibrium with temperature T and chemical
potential mu. We find a master equation for the reduced density operator of the
Bose-Einstein condensate, calculate the steady state of the system and
investigate the effect of one- two- and three particle loss on the condensate.
Using linearized Ito equations we find expressions for the intensity
fluctuations and the amplitude fluctuations in the condensate. A Lorentzian
line shape is found for the intensity correlation function that is
characterized by a time constant gammaI^(-1) derived in the paper. For the
amplitude correlation function we find ballistic behavior for time differences
smaller than gammaI^(-1) and diffusive behavior for larger time differences
