Modeling of stochastic filtration processes in lattice systems

The purpose of the paper was to formulate and study the system of kinetic equations modeling the process of diffusion filtration based on a stochastic approach. Within the research we proved the theorem of existence and uniqueness of the solution with respect to the case of continuous density, obtained the solutions in uniformly convergent and asymptotic series and examined its behavior at infinity. Moreover, we considered the specific cases of density of the Delta-function type and uniform distribution. As a result, the finite-difference scheme for solving the corresponding Cauchy problem on finite time intervals is built and justified. The results of computer simulation are also given.