Time-changes of stochastic processes associated with resistance forms

David Croydon, Ben Hambly, Takashi Kumagai

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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.

Original languageEnglish
Article number82
JournalElectronic Journal of Probability
Volume22
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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