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Your search keyword '"Shaydurov, V."' showing total 3 results
3 results on '"Shaydurov, V."'

1. A finite-difference solution of mean field problem with a predefined control resource.

Author

Kornienko, V. S., Shaydurov, V. V., and Todorov, Michail D

Subjects
*MEAN field theory, *FINITE differences, *PARABOLIC differential equations, *ALGORITHMS, *HAMILTON-Jacobi-Bellman equation
Abstract

The paper presents a computational algorithm for solving problems formulated in terms of Mean Field Game theory with restriction on the control resource. The Mean Field equilibrium leads to a coupled system of two parabolic partial differential equations: Fokker-Planck-Kolmogorov and Hamilton-Jacobi-Bellman ones. The article is devoted to the discrete approximation of these equations. In addition, contrary to other studies, the algorithm constructed here is applicable to problem with more general control function. This algorithm is applied to the problem of heating insulation. [ABSTRACT FROM AUTHOR]

Published
2020
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2. A finite-difference solution of mean field problem with the fractional derivative for subdiffusion.

Author

Shaydurov, V. V., Zhang, S., Kornienko, V. S., and Todorov, Michail D

Subjects
*FINITE differences, *PARABOLIC differential equations, *HAMILTON-Jacobi-Bellman equation, *MEAN field theory, *FOKKER-Planck equation, *RIESZ spaces, *ALGORITHMS
Abstract

The paper presents a computational algorithm for solving problems formulated in terms of Mean Field Game theory with diffusion expressed by fractional derivative. The Mean Field equilibrium leads to a coupled system of two parabolic partial differential equations: modified Fokker-Planck-Kolmogorov and Hamilton-Jacobi-Bellman equations with the highest derivative in space of fractional order less than 2. The article is devoted to the discrete approximation of these equations and the computational algorithm for solving discrete analogues. [ABSTRACT FROM AUTHOR]

Published
2020
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3. Approximations of two-dimensional Mean Field Games with nonsymmetric controls.

Author

Shaydurov, V., Zhang, S., and Kornienko, V.

Subjects
*HAMILTON-Jacobi-Bellman equation, *PARABOLIC differential equations, *CARBON dioxide, *PARABOLIC operators, *NASH equilibrium
Abstract

The numerical methods are presented for solving economic problems formulated in the Mean-Field Game (MFG) form. The mean-field equilibrium is a solution of the coupled system of two parabolic partial differential equations: the Fokker–Planck–Kolmogorov equation and the Hamilton–Jacobi–Bellman one. The description focuses on the discrete approximation of these equations and on the application of the MFG theory directly at discrete level. This approach results in an efficient algorithm for finding the corresponding grid control functions. Contrary to other difference schemes, here the semi-Lagrangian approximation is applied, which improves properties of a discrete problem of this type. This implies the fast convergence of an iterative algorithm for the minimization of the cost functional. The constructed algorithms are implemented to the problem of carbon dioxide pollution. • Mean Field Games describe many events in economics and physics. • They generalize Nash's equilibrium for infinite number of participants (particles). • Special difference schemes inherit properties of Mean Field Game at discrete level. • With these schemes, iterative process for finding the equilibrium is more effective. [ABSTRACT FROM AUTHOR]

Published
2020
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