Hypoellipticity in infinite dimensions and an application in interest rate theory

Authors
Baudoin, Fabrice Teichmann, Josef
Citation
Baudoin, Fabrice et Teichmann, Josef, Hypoellipticity in infinite dimensions and an application in interest rate theory, Annals of applied probability , 15(3), 2005, pp. 1765-1777
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
15
Issue
3
Year of publication
2005
Pages
1765 - 1777
Database
ACNP
SICI code
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.