GENERALIZED BSDES AND NONLINEAR NEUMANN BOUNDARY-VALUE-PROBLEMS

We study a new class of backward stochastic differential equations, wh ich involves the integral with respect to a continuous increasing proc ess. This allows us to give a probabilistic formula for solutions of s emilinear partial differential equations with Neumann boundary conditi on, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.