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

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

2006-05-25

arxiv.org/abs/math/0605658v1

Mathematics

Probability

Scientific paper

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 H\"ormander's
condition. The main new ingredient of the proof is an extension of Norris'
lemma to this situation.

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