English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Standard continuous time random walk (CTRW) models are renewal processes inthe sense that at each jump a new, independent pair of jump length and waitingtime are chosen. Globally, anomalous diffusion emerges through action of thegeneralized central limit theorem leading to scale-free forms of the jumplength or waiting time distributions. Here we present a modified version ofrecently proposed correlated CTRW processes, where we incorporate a power-lawcorrelated noise on the level of both jump length and waiting time dynamics. Weobtain a very general stochastic model, that encompasses key features ofseveral paradigmatic models of anomalous diffusion: discontinuous, scale-freedisplacements as in Levy flights, scale-free waiting times as in subdiffusiveCTRWs, and the long-range temporal correlations of fractional Brownian motion(FBM). We derive the exact solutions for the single-time probability densityfunctions and extract the scaling behaviours. Interestingly, we find thatdifferent combinations of the model parameters lead to indistinguishable shapesof the emerging probability density functions and identical scaling laws. Ourmodel will be useful to describe recent experimental single particle trackingdata, that feature a combination of CTRW and FBM properties.

Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics