H\"ormander-Type Theorem for It\^o Processes and Related Backward SPDEs
  A H\"ormander-type theorem is established for It\^o processes and related backward stochastic partial differential equations (BSPDEs). A short self-contained proof is also provided for the $L^2$-theory of linear, possibly degenerate BSPDEs, in which new gradient estimates are obtained. 
Jinniao Qiu
math.AP