Hypoellipticity in infinite dimensions and an application in interest rate theory

Details Hypoellipticity in infinite dimensions and an application in interest rate theory Hypoellipticity in infinite dimensions and an application in interest rate theory

2005-08-24

arxiv.org/abs/math/0508452v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 1765-1777

Mathematics

Probability

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

Scientific paper

10.1214/105051605000000214

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.

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