Stochastic Analysis and Applications · 2006 · 47 citations · 10 references
EngineeringMathematicsOptimizationStochastic ModelingStochastic ProcessesBoundary ConditionsBoundary-value ProblemsDiffusion ProcessesOptimal StoppingStochastic Differential EquationsStopping TimesBackward Stochastic Differential EquationsLocal TimeNeumann Boundary ConditionsOptimal Stopping For DiffusionsReflected Backward Stochastic Differential EquationsReflecting Boundary ConditionsViscosityViscosity Solutions
In this article, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equation involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary, in using the penalization method. We also give a characterization of the solution as the value function of an optimal stopping time problem. Then we give a probabilistic formula for the viscosity solution of an obstacle problem for PDEs with a nonlinear Neumann boundary condition.
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