The density of the solution to the stochastic transport equation with fractional noise

Christian Olivera (1) , Ciprian Tudor (2)

1 IMECC
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We consider the transport equation driven by the fractional Brownian motion. We study the existence and the uniqueness of the weak solution and, by using the tools of the Malliavin calculus, we prove the existence of the density of the solution and we give Gaussian estimates from above and from below for this density.

Domaines: Probabilités [math.PR]

Christian Olivera, Ciprian Tudor. The density of the solution to the stochastic transport equation with fractional noise. 2014. ⟨hal-01058731⟩