Reflected BSDEs and optimal control and stopping for   infinite-dimensional systems
  We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework. The results are applied to an optimal control and stopping problem. 
Marco Fuhrman, Federica Masiero, Gianmario Tessitore
math.OC