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Transition Probabilities for Symmetric Jump Processes
Authors:Richard F Bass  David A Levin
Institution:Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269 ; Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269
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.

Keywords:Harnack inequality  jump processes  stable processes  Markov chains  transition probabilities
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