Asymptotic behaviour of random walks with correlated temporal structure

DOI10.1098/RSPA.2013.0419zbMath1348.82074OpenAlexW2315736914WikidataQ51143722 ScholiaQ51143722MaRDI QIDQ2831310

Władysław Szczotka, Marcin Magdziarz, Piotr Żebrowski

Publication date: 2 November 2016

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2013.0419

zbMATH Keywords

Langevin equationconvergence in distributionstable distributioncontinuous-time random walksubdiffusionergodicity breaking

Mathematics Subject Classification ID

Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items (11)

Functional convergence of continuous-time random walks with continuous paths ⋮ Generalized diffusion equation associated with a power-law correlated continuous time random walk ⋮ Quenched trap model for Lévy flights ⋮ Nonlinear dynamics of continuous-time random walks in inhomogeneous medium ⋮ Heterogeneous memorized continuous time random walks in an external force fields ⋮ Space-time transport schemes and homogenization. I: general theory of Markovian and non-Markovian processes ⋮ Method of calculating densities for isotropic ballistic Lévy walks ⋮ Asymptotic properties and numerical simulation of multidimensional Lévy walks ⋮ Modeling anomalous diffusion by a subordinated integrated Brownian motion ⋮ Feynman–Kac equation for anomalous processes with space- and time-dependent forces ⋮ Dynamics of a randomly kicked particle

Cites Work

• Langevin picture of Lévy walks and their extensions
• Lagging and leading coupled continuous time random walks, renewal times and their joint limits
• Stochastic representation of subdiffusion processes with time-dependent drift
• Correlated continuous time random walks
• Functional limit theorems for dependent variables
• Multidimensional Lévy walk and its scaling limits
• Fractal solids, product measures and fractional wave equations
• Multidimensional solutions of space–fractional diffusion equations
• Anomalous diffusion in correlated continuous time random walks
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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