Transition Probabilities for Symmetric Jump Processes
Authors:
Richard F. Bass and David A. Levin
Journal:
Trans. Amer. Math. Soc. 354 (2002), 2933-2953
MSC (2000):
Primary 60J05; Secondary 60J35
DOI:
https://doi.org/10.1090/S0002-9947-02-02998-7
Published electronically:
March 11, 2002
MathSciNet review:
1895210
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We consider symmetric Markov chains on the integer lattice in $d$ dimensions, where $\alpha \in (0,2)$ and the conductance between $x$ and $y$ is comparable to $|x-y|^{-(d+\alpha )}$. We establish upper and lower bounds for the transition probabilities that are sharp up to constants.
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Additional Information
Richard F. Bass
Affiliation:
Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269
Email:
bass@math.uconn.edu
David A. Levin
Affiliation:
Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269
Address at time of publication:
P.O. Box 368, Annapolis Junction, Maryland 20701-0368
Email:
levin@member.ams.org
Keywords:
Harnack inequality,
jump processes,
stable processes,
Markov chains,
transition probabilities
Received by editor(s):
June 18, 2001
Received by editor(s) in revised form:
December 27, 2001
Published electronically:
March 11, 2002
Additional Notes:
Research of the first author was partially supported by NSF grant DMS-9988496
Article copyright:
© Copyright 2002
American Mathematical Society
