Smooth density for some nilpotent rough differential equations

Details Smooth density for some nilpotent rough differential equations Smooth density for some nilpotent rough differential equations

2011-04-11

arxiv.org/abs/1104.1972v1

Mathematics

Probability

Contains a Norris type lemma in the rough paths context. A similar result is to be posted soon by M. Hairer and N. Pillai

Scientific paper

In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, whose solution admits a smooth density with respect to Lebesgue's measure. The result is obtained through the use of an explicit representation of the solution when the vector fields of the equation are nilpotent, plus a Norris type lemma in the rough paths context.

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