Pogoruі, А. А. and Rodríguez-Dagnino, Ramón M.
(2015)
The distribution of random motion at non-constant velocity in semi-Markov media.
Random Oper. Stoch. Equ., 1 (1).
pp. 1-13.
Abstract
This paper deals with random motion at non-constant speed with
uniformly distributed directions where the direction alternations occur accord-
ing 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 transi-
tion density near the sphere of its singularity for two- and four-dimensional
cases and variable velocity and the three-dimensional case for constant veloc-
ity. As examples, we have derived the distribution for one-, two- and three-
dimensional random motion
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