Open Access
2017 Time-changes of stochastic processes associated with resistance forms
David Croydon, Ben Hambly, Takashi Kumagai
Electron. J. Probab. 22: 1-41 (2017). DOI: 10.1214/17-EJP99


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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David Croydon. Ben Hambly. Takashi Kumagai. "Time-changes of stochastic processes associated with resistance forms." Electron. J. Probab. 22 1 - 41, 2017.


Received: 12 February 2017; Accepted: 27 August 2017; Published: 2017
First available in Project Euclid: 12 October 2017

zbMATH: 06797892
MathSciNet: MR3718710
Digital Object Identifier: 10.1214/17-EJP99

Primary: 60J35 , 60J55
Secondary: 28A80 , 60J10 , 60J45 , 60K37

Keywords: Bouchaud trap model , FIN diffusion , Fractal , Gromov-Hausdorff convergence , Liouville Brownian motion , Local time , Random conductance model , Resistance form , time-change

Vol.22 • 2017
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