Density estimates on a parabolic SPDE

Abstract

We consider a general class of parabolic spde's

Itô's formula for linear fractional PDEs

“…Now thanks the change of variable v = u−s t 1 −s , the latter integral is finite whenever α < H − 1/4, which, together with (15) and (16), ends the proof.…”

“…And indeed, in case of an equation driven by a Brownian motion, a lot of effort has been made in this direction (let us cite [15,9,8] among others). On the other hand, results concerning SPDEs driven by a fractional Brownian motion are rather scarce (see however [11] for a result on SPDEs with irregular coefficients, and [14] for a study of the Hölder regularity of solutions).…”