Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

DOI10.1088/1742-5468/2014/11/P11031zbMath1456.82784arXiv1402.2772MaRDI QIDQ3301818

Ralf Metzler, Vladimir V. Palyulin, Aleksei V. Chechkin

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2772

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50) Special processes (60K99) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

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First-passage problem for stochastic differential equations with combined parametric Gaussian and Lévy white noises via path integral method ⋮ First passage time moments of asymmetric Lévy flights ⋮ Anomalous diffusion and random search in xyz-comb: exact results ⋮ Existence of cooperative search technique to find a Brownian target ⋮ Search reliability and search efficiency of combined Lévy–Brownian motion: long relocations mingled with thorough local exploration ⋮ Target search of a protein on DNA in the presence of position-dependent bias ⋮ Stochastic dynamics driven by combined Lévy–Gaussian noise: fractional Fokker–Planck–Kolmogorov equation and solution ⋮ Resetting dynamics in a confining potential ⋮ First-passage properties of asymmetric Lévy flights ⋮ Random search on comb

Cites Work

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• Efficient or inaccurate? Analytical and numerical modelling of random search strategies
• Appetitive flight patterns of male \textit{Agrotis segetum} moths over landscape scales
• Lévy flights, non-local search and simulated annealing
• A Guide to First-Passage Processes
• Lévy Processes, Saltatory Foraging, and Superdiffusion
• Record statistics and persistence for a random walk with a drift
• The H-Function
• Scale-free animal movement patterns: Lévy walks outperform fractional Brownian motions and fractional Lévy motions in random search scenarios
• A Method for Simulating Stable Random Variables
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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