Single integro-differential wave equation for Lévy walk
arXiv:1508.04995 · doi:10.1103/PhysRevE.93.020101
Abstract
The integro-differential wave equation for the probability density function for a classical one-dimensional Lévy walk with continuous sample paths has been derived. This equation involves a classical wave operator together with memory integrals describing the spatio-temporal coupling of the Lévy walk. It is valid for any running time PDF and it does not involve any long-time large-scale approximations. It generalizes the well-known telegraph equation obtained from the persistent random walk. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times.
5 pages
References in corpus (6)
- Lévy walks
- Anomalous Diffusion of Inertial, Weakly Damped Particles
- Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
- Asymptotic densities of ballistic Lévy walks
- Transport Equations for Subdiffusion with Nonlinear Particle Interaction
- Persistent random walk of cells involving anomalous effects and random death
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