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We study the asymptotic behaviour of solutions of Forward Backward StochasticDifferential Equations in the coupled case, when the diffusion coefficient ofthe forward equation is multiplicatively perturbed by a small parameter thatconverges to zero. Furthermore, we establish a Large Deviation Principle forthe laws of the corresponding processes.

Forward Backward Stochastic Differential Equations - Asymptotics and a Large Deviations Principle