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A version of Hörmander’s theorem for the fractional Brownian motion. (English) Zbl 1123.60038

Summary: 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.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60G15 Gaussian processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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