Pogoruі, А. А. and RodríguezDagnіno, Ramón М.
(2011)
Isotropic Random Motion at Finite Speed with KErlang
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 KErlang pdf. At first sight, our
generalizations of previous Markovian results appears to be a small step, however, it must
be seen as an important nonMarkovian case where we have found closedform expressions
for the pdf and the conditional characteristic function of this semiMarkov transport process.
We present detailed calculations of a threedimensional example for the 2Erlang 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 2Erlang case can be
extended to a KErlang case (K = 3, 4, . . .) but some of the mathematical expressions may
be cumbersome.
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