Agmon-type estimates for a class of jump processes

• Main Authors: Klein, Markus, Léonard, Christian, Rosenberger, Elke
• Format: Others
• Language: English
• Published: Universität Potsdam 2012
• Subjects: finsler distance; decay of eigenfunctions; jump process; Dirichlet form; Mathematics
• Online Access: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56995; http://opus.kobv.de/ubp/volltexte/2012/5699/

In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space 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 certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.