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2017 Time-changes of stochastic processes associated with resistance forms
David Croydon, Ben Hambly, Takashi Kumagai
Electron. J. Probab. 22(none): 1-41 (2017). DOI: 10.1214/17-EJP99

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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David Croydon. Ben Hambly. Takashi Kumagai. "Time-changes of stochastic processes associated with resistance forms." Electron. J. Probab. 22 1 - 41, 2017. https://doi.org/10.1214/17-EJP99

Information

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

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

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