Forward Backward Stochastic Differential Equations - Asymptotics and a   Large Deviations Principle
  We study the asymptotic behaviour of solutions of Forward Backward Stochastic Differential Equations in the coupled case, when the diffusion coefficient of the forward equation is multiplicatively perturbed by a small parameter that converges to zero. Furthermore, we establish a Large Deviation Principle for the laws of the corresponding processes. 
Ana Bela Cruzeiro and Andr\'e de Oliveira Gomes
math.PR