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In this paper we study a one-dimensional random motion by having a general Erlang distribution for the sojourn times and we obtain higher order hyperbolic equations for this case. We apply the methodology of random evolutions to find the partial differential equations governing the particle motion and we obtain a factorization of these equations. As a particular case we find the linear biwave equation for the symmetric motion case and 2-Erlang distributions for the sojourn times of a semi-Markov evolution.
Key Words: Random evolutions;; semi-Markov processes;; Erlang distributions;; random velocities,; telegrapher's equation,; biwave equation
Published Online: 2005-12-01
Published in Print: 2005-12-01
Copyright 2005, Walter de Gruyter
