In this paper we consider BSDEs with Lipschitz
coefficient reflected on two discontinuous (RCLL) barriers. In this
case, we prove first the existence and uniqueness of the solution,
then we also prove the convergence of the solutions of the penalized
equations to the solution of the RBSDE. Since the method used in the
case of continuous barriers (see Cvitanic and Karatzas, Ann. Probab.24 (1996) 2024–2056 and Lepeltier and San Martín, J. Appl. Probab.41 (2004) 162–175) does not
work, we develop a new method, by considering the solutions of the
penalized equations as the solutions of special RBSDEs and using
some results of Peng and Xu in Annales of I.H.P.41 (2005) 605–630.