The paper proves the flow property of infinite-time mean field FBSDEs, establishes that value functions are viscosity solutions to elliptic master equations at Nash equilibrium, constructs classical solutions via FBSDEs when coefficients are distribution-independent, and shows uniqueness for such P(
Backward stochastic differential equations and quasilinear parabolic partial differential equations,
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Infinite-Time Mean Field FBSDEs and the Associated Elliptic Master Equations
The paper proves the flow property of infinite-time mean field FBSDEs, establishes that value functions are viscosity solutions to elliptic master equations at Nash equilibrium, constructs classical solutions via FBSDEs when coefficients are distribution-independent, and shows uniqueness for such P(