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 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.

Published at http://dx.doi.org/10.1214/105051605000000214 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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