Construction of stationary distribution functions for a system of stochastic Langevin-type equations (Q1079874)

Construction of stationary distribution functions is described which satisfies the Fokker-Planck equation locally in the vicinity of every point and the general non-potential case is considered as well as the case of diffusion tensor degeneration at individual points of the phase space. It is shown that the analysis can be performed by catastrophe theory methods. As an example, a system of Langevin-type equations describing single-mode laser generation is considered.