A version of Hörmander’s theorem for the fractional Brownian motion |
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| Authors: | Fabrice Baudoin Martin Hairer |
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| Affiliation: | (1) Laboratoire de Statistiques et Probabilités, Université Paul Sabatier, 118 Route de Narbonne, Toulouse, France;(2) Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, UK |
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| Abstract: | 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. |
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