The distribution of random motion at non-constant velocity in semi-Markov media

Abstract

This paper deals with random motion at non-constant speed with uniformly distributed directions where the direction alternations occur according to renewal epochs of general distribution. We derive the renewal equation for the characteristic function of the transition density of the multidimensional motion. By using the renewal equation, we study the behavior of the transition density near the sphere of its singularity for two-and four-dimensional cases and variable velocity and the three-dimensional case for constant velocity. As examples, we have derived the distribution for one-, two-and threedimensional random motion.

Solution of Systems of Partial Differential Equations by Using Properties of Monogenic Functions on Commutative Algebras

“…In [6] and [7] this method is applied to the study of one-dimensional distribution of the particles moving in Erlang-2 and Erlang-3 semi-Markov media.…”