Langevin picture of Lévy walks and their extensions

DOI10.1007/S10955-012-0465-2zbMath1243.82034OpenAlexW2065993619MaRDI QIDQ425196

Marcin Magdziarz, Piotr Żebrowski, Władysław Szczotka

Publication date: 7 June 2012

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-012-0465-2

zbMATH Keywords

convergence in distributionsuperdiffusionstable distributionsubdiffusionLévy walkLangevin process

Mathematics Subject Classification ID

Diffusion processes (60J60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items (20)

The influence of the finite velocity on spatial distribution of particles in the frame of levy walk model ⋮ Subordinated continuous-time AR processes and their application to modeling behavior of mechanical system ⋮ Age representation of Lévy walks: partial density waves, relaxation and first passage time statistics ⋮ Functional convergence of continuous-time random walks with continuous paths ⋮ Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario ⋮ Quenched trap model for Lévy flights ⋮ Coupled continuous time random walk with Lévy distribution jump length signifies anomalous diffusion? ⋮ Nonlinear dynamics of continuous-time random walks in inhomogeneous medium ⋮ Lamperti transformation -- cure for ergodicity breaking ⋮ Diffusion limit of Lévy-Lorentz gas is Brownian motion ⋮ Phase diagram in stored-energy-driven Lévy flight ⋮ Limit theorems and governing equations for Lévy walks ⋮ Densities of scaling limits of coupled continuous time random walks ⋮ Asymptotic properties and numerical simulation of multidimensional Lévy walks ⋮ Coupled continuous time-random walks in quenched random environment ⋮ Asymptotic behaviour of random walks with correlated temporal structure ⋮ Feynman–Kac equation for anomalous processes with space- and time-dependent forces ⋮ Limit properties of Lévy walks ⋮ Fractional diffusion equation with distributed-order material derivative. Stochastic foundations ⋮ Selfsimilar diffusions

Cites Work

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• Fractional governing equations for coupled random walks
• Lagging and leading coupled continuous time random walks, renewal times and their joint limits
• Stochastic representation of subdiffusion processes with time-dependent drift
• Random walks with infinite spatial and temporal moments
• Can one see \(\alpha\)-stable variables and processes?
• Limit theorems for coupled continuous time random walks.
• Langevin picture of subdiffusion with infinitely divisible waiting times
• Stochastic-Process Limits
• Stochastic solution of space-time fractional diffusion equations
• Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma
• Cluster continuous time random walks
• On fully coupled continuous time random walks
• Path Properties of Subdiffusion—A Martingale Approach
• Some Useful Functions for Functional Limit Theorems
• Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
• Anomalous diffusion in correlated continuous time random walks
• Short and Long Memory Fractional Ornstein–Uhlenbeck α-Stable Processes
• Limit theorems for randomly coarse grained continuous-time random walks
• First Steps in Random Walks
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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