Affiliation:
1. Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wroclaw University of Science and Technology Wyspianskiego 27, 50-370 Wroclaw, Poland
Abstract
Abstract
In this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer G-function. This allows to efficiently evaluate them numerically. We also compute two-point distribution of wait-first model. Our results show perfect agreement with the Monte Carlo simulations.
Subject
Applied Mathematics,Analysis
Reference43 articles.
1. M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York, Dover (1972), 555–566.
2. D. Applebaum, Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge (2004).
3. E. Barkai, Y-C. Cheng, Aging continuous time random walks. J. Chem. Phys.118, No 14 (2003), 6167–6178; 10.1063/1.1559676.
4. P. Barthelemy, P.J. Bertolotti, D.S. Wiersma, A Lévy flight for light. Nature453, No 7194 (2008), 495–498; 10.1038/nature06948.
5. P. Becker-Kern, M. M. Meerschaert, H.-P. Scheffler, Limit theorems for coupled continuous time random walks. Ann. Prob.32, No 1B (2004), 730–756.
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