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Reflected forward-backward stochastic differential equations and related PDEs. (English) Zbl 1347.60070

Summary: In this article, we study a type of coupled reflected forward-backward stochastic differential equations (reflected FBSDEs, for short) with continuous coefficients, including the existence and the uniqueness of the solution of our reflected FBSDEs as well as a comparison theorem. We prove that the solution of our reflected FBSDEs gives a probabilistic interpretation for the viscosity solution of an obstacle problem for a quasilinear parabolic partial differential equation.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
35D40 Viscosity solutions to PDEs
35K59 Quasilinear parabolic equations
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