Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions

Fabrice Baudoin, Cheng Ouyang, Samy Tindel

Published 2011-04-19Version 1

In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfy the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case H > 1/3 and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper sub-Gaussian bound.