Stochastic modelling of fractal diffusion and dimension estimation

František Gašpar and Jaromír Kukal

Physica A: Statistical Mechanics and its Applications, 2022, vol. 602, issue C

Abstract: The revision of classical methods for spectral and walk dimension estimates is the main aim of the paper. Being focused on the unbiased estimation of the walk and spectral dimensions, we aim to construct the estimates with the minimal mean square error. Accompanied simulation experiments are performed on finite substrates, spacial structures serving as a good model of both continuum and fractal sets. We compare the classical approach based on the log–log transform of asymptotic models of returning probabilities and the second moments, and we also develop a weighted approach to improve the statistical properties of dimension estimates. The other discussed aspect is whether to simulate diffusion using the classical graph diffusion model with zero probability of staying in the same vertex or to prefer the physically motivated model of diffusion over edges with the optimal value of jump probability. Finally, we present the results of simulation experiments on two-dimensional finite substrates which approximate the continuum and selected Sierpinski gaskets and carpets. The paper also summarises general suggestions based on the obtained results from the simulation experiments.

Keywords: Diffusion modelling; Dimension estimation; Fractal substrate; Graph representation; Spectral dimension; Walk dimension (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:602:y:2022:i:c:s037843712200423x

DOI: 10.1016/j.physa.2022.127624

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