Exact solutions for isotropic random flights in odd dimensions (Q2872325)

The Pearson random walk was studied very well and generalized to any integer as well as non-integer dimensions. In the dimension three, this is known as the Rayleigh's random flight. In the reviewed paper, a method of solving the isotropic random flight in arbitrary dimension was presented. Namely, in odd dimensions, it was shown that the probability density can be written by a piecewise polynomial function. The method is based on the fact that the projection of an isotropic function has an inverse and the convolution commutes with the projection and the inverse projection. Up to the dimension five, the explicit formulas for the probability density were derived.