title: Explicit densities of multidimensional ballistic Lévy walks.
abstract: Lévy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real-life phenomena. In this paper we derive explicit formulas for densities of the two- (2D) and three-dimensional (3D) ballistic Lévy walks, which are most important in applications. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D Lévy walks are expressed in terms of hypergeometric functions and the right-side Riemann-Liouville fractional derivative, which allows us to efficiently evaluate them numerically. The theoretical results agree perfectly with Monte Carlo simulations.
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
authors.forename: Marcin
authors.initials: M
authors.lastname: Magdziarz
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Zorawik