For citation:
Arutyunyan R. V. Stochastic Simulation of Diffusion Filtering. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 1, pp. 5-12. DOI: 10.18500/1816-9791-2016-16-1-5-12, EDN: VUSOCT
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.Thefinite-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.
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