Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media (d > 1), where the particle can move along 2 d directions. We derive the equations for the probability density function using the " formulae of differentiation " of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.