  We derive a stochastic process that describes the kinetics of a
one-dimensional Bose gas in a regime where three body collisions are important.
In this situation the system becomes non integrable offering the possibility to
investigate dissipative phenomena more simply compared to higher dimensional
gases. Unlike the quantum Boltzmann equation describing the average momentum
distribution, the stochastic approach allows a description of higher-order
correlation functions in a canonical ensemble. As will be shown, this ensemble
differs drastically from the grand canonical one. We illustrate the use of this
method by determining the time evolution of the momentum mode particle number
distribution and the static structure factor during the evaporative cooling
process.
