On Numerical Approximations of Fractional and Nonlocal Mean Field Games

Chowdhury Indranil; Ersland Olav; Jakobsen Espen R.

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On Numerical Approximations of Fractional and Nonlocal Mean Field Games

机译：On Numerical Approximations of Fractional and Nonlocal Mean Field Games

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Abstract We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the distributions of agents. The methods are monotone, stable, and consistent, and we prove convergence along subsequences for (i) degenerate equations in one space dimension and (ii) nondegenerate equations in arbitrary dimensions. We also give results on full convergence and convergence to classical solutions. Numerical tests are implemented for a range of different nonlocal diffusions and support our analytical findings.

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《Foundations of computational mathematics》 |2023年第4期|1381-1431|共51页
作者
Chowdhury Indranil; Ersland Olav; Jakobsen Espen R.;
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作者单位

University of Zagreb;

Norwegian University of Science and Technology;

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原文格式 PDF
正文语种英语
中图分类应用数学;
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Mean field games; Jump diffusion; Anomalous diffusion; Nonlocal operators; Fractional PDEs; Nonlocal PDEs; Degenerate PDEs; Semi-Lagrangian scheme; Convergence; Compactness; Fokker–Planck equations; Hamilton–Jacobi–Bellman equations; Duality methods; 35Q89; 47G20; 35Q84; 49L12; 45K05; 35K61; 65M12; 91A16; 65M22; 35R11; 35R06;

On Numerical Approximations of Fractional and Nonlocal Mean Field Games

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