On the Malliavin differentiability of BSDEs
  In this paper we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. Our results rely on the interpretation of the Malliavin derivative as a G{\^a}teaux derivative in the directions of the Cameron-Martin space. Incidentally, we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces $D^{1,p}$ . 
Thibaut Mastrolia, Dylan Possama\"i, Anthony R\'eveillac
math.PR