Hypoellipticity in infinite dimensions and an application in interest rate theory

Abstract

We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hörmander’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 Hörmander condition, have the conceptually undesirable feature that any selection of yields admits a density as multi-dimensional random variable.