Pogoruі, А. А. and RodríguezDagnino, Ramón M.
(2015)
The distribution of random motion at nonconstant velocity in semiMarkov media.
Random Oper. Stoch. Equ., 1 (1).
pp. 113.
Abstract
This paper deals with random motion at nonconstant 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 fourdimensional
cases and variable velocity and the threedimensional case for constant veloc
ity. As examples, we have derived the distribution for one, two and three
dimensional random motion
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