Hypoellipticity in infinite dimensions and an application in interest rate theory

2005/07/15 by Fabrice Baudoin, Josef Teichmann · 3 citations
Economics, Econometrics and Finance · Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60H07 #msc:60H10 #msc:60H30

paper · pdf · doi:10.1214/105051605000000214

published as Annals of Applied Probability 2005, Vol. 15, No. 3, 1765-1777 · 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)

openalex publication_date 2005/07/15 · arxiv created 2005/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Existence of Lévy term structure models
• Existence of densities for stochastic evolution equations driven by fractional Brownian motion
• On Malliavinʼs proof of Hörmanderʼs theorem

Related

• Hypoellipticity in Infinite Dimensions
• Finite dimensional Realizations of Stochastic Equations
• Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise
• Hörmander's hypoelliptic theorem for nonlocal operators
• Hörmander's theorem for stochastic partial differential equations