  This paper proposes a new method to propagate uncertainties undergoing
nonlinear dynamics using the Koopman Operator (KO). Probability density
functions are propagated directly using the Koopman approximation of the
solution flow of the system, where the dynamics have been projected on a
well-defined set of basis functions. The prediction technique is derived
following both the analytical (Galerkin) and numerical (EDMD) derivation of the
KO, and a least square reduction algorithm assures the recursivity of the
proposed methodology.
