Diffusion processes on fractal fields: Heat kernel estimates and large deviations

B. M. Hambly*, T. Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

A fractal field is a collection of fractals with, in general, different Hausdorff dimensions, embedded in ℝ2. We will construct diffusion processes on such fields which behave as Brownian motion in ℝ2 outside the fractals and as the appropriate fractal diffusion within each fractal component of the field. We will discuss the properties of the diffusion process in the case where the fractal components tile ℝ2. By working in a suitable shortest path metric we will establish heat kernel bounds and large deviation estimates which determine the trajectories followed by the diffusion over short times.

Original languageEnglish
Pages (from-to)305-352
Number of pages48
JournalProbability Theory and Related Fields
Volume127
Issue number3
DOIs
Publication statusPublished - 2003 Nov
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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