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We use the quantum kinetic theory to calculate the steady state and thefluctuations of a trapped Bose-Einstein condensate at finite temperature. Thesystem is divided in a condensate and a non-condensate part. A quantummechanical description based on the number conserving Bogoliubov method is usedfor describing the condensate part. The non-condensed particles are treated asa classical gas in thermal equilibrium with temperature T and chemicalpotential mu. We find a master equation for the reduced density operator of theBose-Einstein condensate, calculate the steady state of the system andinvestigate the effect of one- two- and three particle loss on the condensate.Using linearized Ito equations we find expressions for the intensityfluctuations and the amplitude fluctuations in the condensate. A Lorentzianline shape is found for the intensity correlation function that ischaracterized by a time constant gammaI^(-1) derived in the paper. For theamplitude correlation function we find ballistic behavior for time differencessmaller than gammaI^(-1) and diffusive behavior for larger time differencesComment: 15 pages with 7 figures to appear in Phys. Rev.

Quantum kinetic theory. IV. Intensity and amplitude fluctuations of a Bose-Einstein condensate at finite temperature including trap loss