Isotropic random flights

The probability density of distribution function of the sum of N isotropic random vectors is studied for the general case in which the probability density of the lengths of the individual vectors vanishes identically outside a finite interval. The probability density function is expressed in a Fourier sine series whose coefficients are the sampled values of the characteristic function. Typical numerical calculations are summarized in graphical form for the case where the lengths of the vectors obey a rectangular probability density. Sampling expansions are also developed for the moments and the distribution function.