Known Girsanov and Bismut-Elworthy-Li identities are recast as explicit grid-free Monte Carlo algorithms for coupled Fokker-Planck and Hamilton-Jacobi-Bellman systems, with a neural-network demonstration on a Schrödinger bridge problem.
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On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
Known Girsanov and Bismut-Elworthy-Li identities are recast as explicit grid-free Monte Carlo algorithms for coupled Fokker-Planck and Hamilton-Jacobi-Bellman systems, with a neural-network demonstration on a Schrödinger bridge problem.