Agmon-type estimates for a class of jump processes
Probability
2013-09-17 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
In the limit epsilon to 0 we analyze the generators H_epsilon of families of reversible jump processes in R^d 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 C^2 or just Lipschitz. Our estimates are analog to the semi-classical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice epsilon Z^d. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.
Keywords
Cite
@article{arxiv.1309.3918,
title = {Agmon-type estimates for a class of jump processes},
author = {Markus Klein and Christian Leonard and Elke Rosenberger},
journal= {arXiv preprint arXiv:1309.3918},
year = {2013}
}