Summary.
We study a new class of backward stochastic differential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial differential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.
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Received: 27 September 1996 / In revised form: 1 December 1997
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Pardoux, E., Zhang, S. Generalized BSDEs and nonlinear Neumann boundary value problems. Probab Theory Relat Fields 110, 535–558 (1998). https://doi.org/10.1007/s004400050158
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DOI: https://doi.org/10.1007/s004400050158