Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation
Giuseppe Da Prato, Arnaud Debussche · arXiv (Cornell University) · 2015
We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_tDφ$ in terms of $\|φ\|_{L^2(H,ν)}$, where $ν$ is the invariant measure of $P_t$.