The Annals of Applied Probability

Hypoellipticity in infinite dimensions and an application in interest rate theory

Fabrice Baudoin and Josef Teichmann

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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.

Article information

Source
Ann. Appl. Probab. Volume 15, Number 3 (2005), 1765-1777.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1121433768

Digital Object Identifier
doi:10.1214/105051605000000214

Mathematical Reviews number (MathSciNet)
MR2152244

Zentralblatt MATH identifier
1081.60039

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Generic evolutions in interest rate theory HJM equations Hörmander’s theorem Malliavin calculus hypoellipticity

Citation

Baudoin, Fabrice; Teichmann, Josef. Hypoellipticity in infinite dimensions and an application in interest rate theory. Ann. Appl. Probab. 15 (2005), no. 3, 1765--1777. doi:10.1214/105051605000000214. http://projecteuclid.org/euclid.aoap/1121433768.


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