Some Functional Inequalities for Stochastic Differential Equations Driven by Brownian Motions

Fractional Brownian motion is a natural generalization of Brownian motion. Study of stochastic differential equations (SDEs) driven by fractional Brownian motions has been an active area in current research, as it provides a concrete application of the rough path theory, an integration theory developed recently.

In this talk, I will present some functional inequalities for SDEs driven by fractional Brownian motions. In particular, we show a concentration inequality for the law of solution to such SDEs. As a consequence of the concentration inequality, we obtain a Gaussian upper bound for the density of the solution. The presentation is based on a joint work with F. Baudoin and S. Tindel.