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

2006/05/25 by F. Baudoin, Baudoin, F., M. Hairer +1 · 1 citation
Mathematics · #60G30 #60H07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G30 #msc:60H07

paper · pdf · doi:10.48550/arxiv.math/0605658

arxiv created 2006/05/25 · arxiv updated 2009/12/01

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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• Fractional Diffusion Bridges

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