Infinite ergodic theory for heterogeneous diffusion processes
Infinite ergodic theory for heterogeneous diffusion processes
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim |x-\tilde{x}|^{2-2/\alpha}$ in the vicinity of a point $\tilde{x}$, where $\alpha$ can be either positive or negative. We find …