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Transition Probabilities for Symmetric Jump Processes

Author(s): Richard F. Bass; David A. Levin
Journal: Trans. Amer. Math. Soc. 354 (2002), 2933-2953.
MSC (2000): Primary 60J05; Secondary 60J35
Posted: March 11, 2002
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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 $\vert x-y\vert^{-(d+\alpha )}$. 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

DOI: 10.1090/S0002-9947-02-02998-7
PII: S 0002-9947(02)02998-7
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
Posted: March 11, 2002
Additional Notes: Research of the first author was partially supported by NSF grant DMS-9988496
Copyright of article: Copyright 2002, American Mathematical Society

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