Agmon-type estimates for a class of jump processes

  • 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.

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Author:Markus Klein, Christian Léonard, Elke Rosenberger
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1 (2012) 6)
Document Type:Preprint
Date of Publication (online):2012/01/06
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/01/06
Tag:Dirichlet form; decay of eigenfunctions; finsler distance; jump process
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:31-XX POTENTIAL THEORY (For probabilistic potential theory, see 60J45) / 31Cxx Other generalizations / 31C25 Dirichlet spaces
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G99 None of the above, but in this section
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990 , SK 540