Hypoellipticity in infinite dimensions and an application in interest   rate theory
  We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate theory, which satisfy the Hormander condition, have the conceptually undesirable feature that any selection of yields admits a density as multi-dimensional random variable. 
Fabrice Baudoin and Josef Teichmann