A diffusion process for the asymptotic limit of a noncentred stochastic system

The diffusion effects of solution processes for a large class of stochastic equations have been characterized by Khasminskii's limit theory. Compared to either the Ito or the Stratonovich interpretation of stochastic differential equations, this theory has been effective from a modelling point of view in that the drift coefficient of the resultant Kolmogorov backward equation may include a term from the centred random field. A noncentred stochastic system on an asymptotically infinite interval is studied in this article on the basis of the limit theory and it is motivated by a singular behaviour of classical waves in a random multilayer. The extended Kolmogorov-Fokker-Planck equation for the transition probability density is derived and the solution of this equation is represented by an explicit approximate form based upon the pseudodifferential operator theory and Wiener's path integral representation.