Pogoruі, А. А. and Rodríguez-Dagnіno, Ramón М.
(2011)
Isotropic Random Motion at Finite Speed with K-Erlang
Distributed Direction Alternations.
Springer Science+Business Media.
Abstract
We study uniformly distributed direction ofmotion at finite speed where the direction
alternations occur according to the renewal epochs of a K-Erlang pdf. At first sight, our
generalizations of previous Markovian results appears to be a small step, however, it must
be seen as an important non-Markovian case where we have found closed-form expressions
for the pdf and the conditional characteristic function of this semi-Markov transport process.
We present detailed calculations of a three-dimensional example for the 2-Erlang case,
which is important not only from physical applications point of view but also to understand
more general models. For instance, in principle the example of the 2-Erlang case can be
extended to a K-Erlang case (K = 3, 4, . . .) but some of the mathematical expressions may
be cumbersome.
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