Under the hypothesis of convergence in probability of a sequence of càdlàg processes (X n ) n to a càdlàg process X, we are interested in the convergence of corresponding values in optimal stopping and also in the convergence of optimal stopping times. We give results under hypothesis of inclusion of filtrations or convergence of filtrations.

Abstract. In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if (W n ) is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion W and if (τ n ) is a sequence of stopping times that converges to a stopping time τ , then the solution of the BSDE driven by W n with random terminal time τ n converges to the solution of the BSDE driven by W with random terminal time τ .Mathematics Subject Classification. 60H10, 60Fxx, 60G40.

Abstract. This paper is a corrigendum to paper Toldo, ESAIM, P&S 10 (2006) 141-163 where we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time.Mathematics Subject Classification. 60H10, 60Fxx, 60G40.