The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.
Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.
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