Electronic Journal of Probability

Time-changes of stochastic processes associated with resistance forms

David Croydon, Ben Hambly, and Takashi Kumagai

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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.

Article information

Electron. J. Probab. Volume 22 (2017), paper no. 82, 41 pp.

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

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Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J55: Local time and additive functionals
Secondary: 28A80: Fractals [See also 37Fxx] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60K37: Processes in random environments

Bouchaud trap model FIN diffusion fractal Gromov-Hausdorff convergence Liouville Brownian motion local time random conductance model resistance form time-change

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Croydon, David; Hambly, Ben; Kumagai, Takashi. Time-changes of stochastic processes associated with resistance forms. Electron. J. Probab. 22 (2017), paper no. 82, 41 pp. doi:10.1214/17-EJP99. https://projecteuclid.org/euclid.ejp/1507795233

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