  We present a stochastic method for the simulation of the time evolution in
systems which obey generalized statistics, namely fractional exclusion
statistics and Gentile's statistics. The transition rates are derived in the
framework of canonical ensembles. This approach introduces a tool for
describing interacting fermionic and bosonic systems in non-equilibrium as
ideal FES systems, in a computationally efficient manner. The two types of
statistics are analyzed comparatively, indicating their intrinsic thermodynamic
differences and revealing key aspects related to the species size.
