First passage time moments of asymmetric Lévy flights

Abstract

We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in a semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage time probability density function for different values of the index of stability and the skewness parameter. A comparison with results using the Langevin approach to Lévy flights is presented. For the semi-infinite domain, in certain special cases analytic results are derived explicitly, and in bounded intervals a general analytical expression for the mean first-passage time of Lévy flights with arbitrary skewness is presented. These results are complemented with extensive numerical analyses.

arXiv comment47 pages, 13 figures, IOP LaTeX

References in corpus (41)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Forecast and Control of Epidemics in a Globalized World
• Levy Flights, Non-local Search and Simulated Annealing
• Ten equivalent definitions of the fractional Laplace operator
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Fractional Laplacian in Bounded Domains
• Optimal target search on a fast folding polymer chain with volume exchange
• Lévy flights in random environments
• First passages in bounded domains: When is the mean first passage time meaningful?
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Leapover lengths and first passage time statistics for Lévy flights
• First passages for a search by a swarm of independent random searchers
• Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
• Lévy flights in a steep potential well
• Levy--Brownian motion on finite intervals: Mean first passage time analysis
• Distance matters: the impact of gene proximity in bacterial gene regulation
• First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Survival of an evasive prey
• Fractional Diffusion Equation for a Power-Law-Truncated Levy Process
• First-passage and first-hitting times of Levy flights and Levy walks
• Lévy Noise Induced Switch in the Gene Transcriptional Regulatory System
• The problem of analytical calculation of barrier crossing characteristics for Levy flights
• Group chasing tactics: how to catch a faster prey?
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells
• Codifference as a practical tool to measure interdependence
• Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
• Hitting distributions of alpha-stable processes via path censoring and self-similarity
• On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations
• Search reliability and search efficiency of combined Lévy-Brownian motion: long relocations mingled with thorough local exploration
• Survival Probability of Random Walks and Lévy Flights on a Semi-Infinite Line
• Probability density of the fractional Langevin equation with reflecting walls
• On the kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts
• Optimization of random search processes in the presence of an external bias
• Comparison of pure and combined search strategies for single and multiple targets
• Anomalous Infiltration
• A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
• The Spectrum of the Fractional Laplacian and First Passage Time Statistics
• Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

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