On Random Flights with Non-uniformly Distributed Directions

This paper deals with a new class of random flights in ℝ ^d , d≥2, characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature where the directions are taken according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter ν≥0, which gives the anisotropy of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function.