2018
Том 70
№ 11

Multidimensional random motion with uniformly distributed changes of direction and Erlang steps

Abstract

In this paper we study transport processes in $\mathbb{R}^n,\quad n \geq 1$, 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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 4, pp 665-671.

Citation Example: Pogorui A. О., Rodriguez-Dagnino R. M. Multidimensional random motion with uniformly distributed changes of direction and Erlang steps // Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 572-577.

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