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

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.

References in corpus (1)

• Self-similarity and fractional Brownian motions on Lie groups

Cited by in corpus (5)

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• On the Variational Regularity of Cameron-Martin paths
• Local times of stochastic differential equations driven by fractional Brownian motions