Two-level diffusion, random walk and uniqueness

A nonsymmetric random walk is used as a model of diffusion with drift, in a double manner, using both a description by moments and a difference equation. It is observed that the diffusion coefficients obtained by both methods are different, and become equal only in the limit of small asymmetry of the random walk. After passing from differences to differentials Streaterʹs two-level diffusion equations are obtained. Next, two-level diffusion described by this system of differential equations is discussed, and the uniqueness of its solution is studied. Finally, the equations for the density functions of a two-level system are separated into equations for each density.