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arXiv · 1609.02120

Time-changes of stochastic processes associated with resistance forms

D. A. Croydon·B. M. Hambly·T. Kumagai
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Abstract

Given a sequence of resistance forms that converges with respect to the Gromov-Hausdorff-vague topology and satisfies a uniform volume doubling condition, we show the convergence of corresponding Brownian motions and local times. As a corollary of this, we obtain the convergence of time-changed processes. Examples of our main results include scaling limits of Liouville Brownian motion, the Bouchaud trap model and the random conductance model on trees and self-similar fractals. For the latter two models, we show that under some assumptions the limiting process is a FIN diffusion on the relevant space.

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D. A. Croydon, B. M. Hambly, T. Kumagai. 2016-09-07. Time-changes of stochastic processes associated with resistance forms. https://arxiv.org/abs/1609.02120

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