  New partial differential equations for the Wiener-Hermite expansions of the
Langevin (stochastic) transitions are formulated. They are solved recursively
in full order series solutions with respect to $\sqrt{t}$. A sort of 'gauge'
degrees of freedom (arbitrariness) involved in the solutions are analyzed and
clarified. The Wiener-Hermite expansions play important roles as basic elements
of numerical simulations of the Langevin equations. Specific solutions within
some orders are presented as examples. These expansions giving integral
representations of the Fokker-Planck evolution kernels, similar formulations
are possible for the imaginary time Hamiltonian evolution kernels as well.
