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Beyond separability: Convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability

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  • Yu, Winston
  • Du, Qiang
  • Tang, Wenpin

Abstract

We study the vanishing viscosity approximation to mean field games (MFGs) in Rd with a nonlocal and possibly non-separable Hamiltonian. We prove that the value function converges at a rate of O(β), where β2 is the diffusivity constant, which matches the classical convergence rate of vanishing viscosity for Hamilton-Jacobi (HJ) equations. The same rate is also obtained for the approximation of the distribution of players as well as for the gradient of the value function. The proof is a combination of probabilistic and analytical arguments by first analyzing the forward-backward stochastic differential equation associated with the MFG, and then applying a general stability result for HJB equations. Applications of our result to N-player games, mean field control, and policy iteration for solving MFGs are also presented.

Suggested Citation

  • Yu, Winston & Du, Qiang & Tang, Wenpin, 2026. "Beyond separability: Convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability," Stochastic Processes and their Applications, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:spapps:v:201:y:2026:i:c:s0304414926001936
    DOI: 10.1016/j.spa.2026.105061
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