A Sobolev inequality and the individual invariance principle for diffusions in a periodic potential

Moustapha Ba, Pierre Mathieu

We consider a diffusion process in ${\mathbb{R}}^d$ with a generator of the form $L:=\frac{1}{2}{e}^{V(x)}div(e^{-V(x)}\nabla )$ where $V$ is measurable and periodic. We only assume th…