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The recently proposed numerical algorithm, deep BSDE method, has shownremarkable performance in solving high-dimensional forward-backward stochasticdifferential equations (FBSDEs) and parabolic partial differential equations(PDEs). This article lays a theoretical foundation for the deep BSDE method inthe general case of coupled FBSDEs. In particular, a posteriori errorestimation of the solution is provided and it is proved that the errorconverges to zero given the universal approximation capability of neuralnetworks. Numerical results are presented to demonstrate the accuracy of theanalyzed algorithm in solving high-dimensional coupled FBSDEs.

Convergence of the Deep BSDE Method for Coupled FBSDEs