New exact solutions to the Fokker–Planck–Kolmogorov equation

A generalized Liouville theorem has been proven for Itô systems. This allows us to show that the conserved quantities of the deterministic part of the Itô systems lead to the solution of the Fokker–Planck–Kolmogorov equation. The results have been applied to a stochastic 3-species Lotka Volterra system and the semi-classical Jaynes–Cummings system.