Stability of parabolic Harnack inequalities

Let (G,E) be a graph with weights \{a_{xy}\} for which a parabolic Harnack inequality holds with space-time scaling exponent \beta \ge 2. Suppose \{a'_{xy}\} is another set of weights that are comparable to \{a_{xy}\}. We prove that this parabolic Harnack inequality also holds for (G,E) with th...

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Bibliographic Details
Published in:	Transactions of the American Mathematical Society Vol. 356; no. 4; pp. 1501 - 1533
Main Authors:	Barlow, Martin T., Bass, Richard F.
Format:	Journal Article
Language:	English
Published:	Providence, RI American Mathematical Society 01-04-2004
Subjects:	Brownian motion Exact sciences and technology Fractals General mathematics General, history and biography Markov chains Mathematical functions Mathematical inequalities Mathematical theorems Mathematics Random walk Sciences and techniques of general use Spacetime Transition probabilities Vertices Harnack inequality volume doubling random walks on graphs Green functions anomalous diffusion Sobolev inequality Poincaré inequality Space time Mathematics Necessary and sufficient condition Numerical stability
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Summary:	Let (G,E) be a graph with weights \{a_{xy}\} for which a parabolic Harnack inequality holds with space-time scaling exponent \beta \ge 2. Suppose \{a'_{xy}\} is another set of weights that are comparable to \{a_{xy}\}. We prove that this parabolic Harnack inequality also holds for (G,E) with the weights \{a'_{xy}\}. We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.
ISSN:	0002-9947 1088-6850
DOI:	10.1090/S0002-9947-03-03414-7