A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
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The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.
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Numerical analysis of first-order mean field games under displacement monotonicity
A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
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Implementation of Milstein Schemes for Stochastic Delay-Differential Equations with Arbitrary Fixed Delays
The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.