Probability Theory and Related Fields

, Volume 139, Issue 3–4, pp 373–395 | Cite as

A version of Hörmander’s theorem for the fractional Brownian motion

  • Fabrice Baudoin
  • Martin HairerEmail author


It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hörmander’s condition. The main new ingredient of the proof is an extension of Norris’ lemma to this situation.


Stochastic Differential Equation Fractional Brownian Motion Gaussian Measure Carnot Group Hurst Parameter 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Laboratoire de Statistiques et ProbabilitésUniversité Paul SabatierToulouseFrance
  2. 2.Mathematics InstituteThe University of WarwickCoventryUK

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