Generalized Snell Envelope as a Minimal Solution of BSDE With Lower   Barriers
  The aim of this paper is to characterize the Snell envelope of a given P-measurable process l as the minimal solution of some backward stochastic differential equation with lower general reflecting barriers and to prove that this minimal solution exists. 
E. H. Essaky, M. Hassani, Y. Ouknine
math.PR