We will present in this talk a mathematical result concerning a stochastic model used by physicist to describe Bose Einstein Condensation at finite temperature. We will give a talk on the convergence to the Gibbs equilibrium, and the global existence of solutions a.s. with respect to the Gibbs measure. This is a joint work with Anne de Bouard (Ecole polytechnique, France) and Arnaud Debussche (ENS Rennes, France).