Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions gr eater than 1. Based on a cubic lattice, the model is suitable for an arbitr ary dimension d. We study the continuum limit and obtain the equation satis fied by the probability density function for the position of the random wal ker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegrapher's equation, may open a new way to address the p roblem of light propagation through thin slabs. [S1063-651X(98)00312-2].