Multidimensional random motion with uniformly distributed changes of direction and Erlang steps - Pogorui A. О.; Rodriguez-Dagnino, R. M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
In this paper we study transport processes in R^n,n ≥ 1, having non-exponential distributed sojourn times or non-Markovian step durations. We use the idea that the probabilistic properties of a random vector are completely determined by those of its projection on a fixed line, and using this idea we avoid many of the difficulties appearing in the analysis of these problems in higher dimensions. As a particular case, we find the probability density function in three dimensions for 2-Erlang distributed sojourn times.