  We consider the use of a Kinetic Monte Carlo approach for the description of
non-equilibrium bosonic systems, taking non-resonantly excited
exciton-polariton condensates and bosonic cascade lasers as examples. In the
former case, the considered approach allows the study of the cross-over between
incoherent and coherent regimes, which represents the formation of a
quasi-condensate that forms purely from the action of energy relaxation
processes rather than interactions between the condensing particles themselves.
In the latter case, we show that a bosonic cascade can theoretically develop an
output coherent state.
