Stochastic simulation of diffusion filtering

Formulated and investigated is the system of kinetic equations describing the process of diffusion filtering based on a stochastic approach. The theorem of existence and uniqueness of the solution for the case of a continuous density is prove. We obtain the representation of solution in the form of a uniformly convergent and asymptotic series, and explore the nature of its behavior at infinity. The concrete particular cases such as the density of the delta function and a uniform distribution are considered. The finite-difference scheme for the solution of the corresponding Cauchy problem on finite intervals of time is constructed and justified. The results of computer simulation are given.