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Time-changes of stochastic processes associated with resistance forms · Around

2016

Time-changes of stochastic processes associated with resistance forms

Croydon, D. A., Hambly, B. M., Kumagai, T.

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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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1968
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