Ordered cumulant technique and differential equations for probability density

This paper is concerned with stochastic differential equations of Langevin type in which the stochastic forces are gaussian and not of white noise type. The problem of finding explicitly the differential equation for the probability density of the process is solved by means of an expansion in the small correlation time of the noise. For this purpose we will use the cumulant technique. Different situations are studied such as: markovian or Fokker-Planck equation, first correction to the markovian approximation but with the Fokker-Planck form and the corrections of non-Fokker-Planck form.