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Hypoellipticity in infinite dimensions and an application in interest rate theory

Research paper by Fabrice Baudoin, Josef Teichmann

Indexed on: 24 Aug '05Published on: 24 Aug '05Published in: Mathematics - Probability



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.