A probabilistic approach to large time behaviour of mild solutions of   Hamilton-Jacobi-Bellman equations in infinite dimension
  We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial time behaves like a linear term in $T$ shifted with the solution of the associated EBSDE taken at initial time. Moreover we give an explicit speed of convergence, which seems to appear very rarely in literature. 
Ying Hu (IRMAR), Pierre-Yves Madec (IRMAR), Adrien Richou
math.PR