Geodesic
Stochastic simulation of diffusion filtering
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 5-12

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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. 
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     author = {R. V. Arutyunyan},
     title = {Stochastic simulation of diffusion filtering},
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     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a0/}
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R. V. Arutyunyan. Stochastic simulation of diffusion filtering. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 5-12. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a0/