Agmon-type estimates for a class of jump processes

In the limit <tex>\varepsilon \to 0</tex> we analyze the generators <tex>H_\varepsilon</tex> of families of reversible jump processes in <tex>R^d </tex>associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions.

The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being <tex>C^2</tex> or just Lipschitz.
Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice <tex>\varepsilon Z^d</tex>.

Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.