Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Stability of parabolic Harnack inequalities

Auteur(s):

Code(s) de Classification MSC:

• 60J27 Markov chains with continuous parameter
Résumé: 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 necessary and sufficient conditions for this parabolic Harnack inequality to hold.