Method of calculating densities for isotropic ballistic Lévy walks

We provide explicit formulas for asymptotic densities of d-dimensional (d > 1) isotropic Lévy walks in a ballistic regime. The densities of multidimensional undershooting and overshooting Lévy walks are presented as well. Interestingly, when the number of dimensions is odd the densities of all these Lévy walks are given by elementary functions. When d is even, we can express the densities as fractional derivatives of hypergeometric functions, which makes an efficient numerical evaluation possible. A simulation algorithm for isotropic Lévy walks is presented as well. The theoretical results are in agreement with the results of Monte Carlo simulations.