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Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations

Abstract

We study uniformly distributed direction of motion 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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Correspondence to Ramón M. Rodríguez-Dagnino.

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Grant CAT148 from Tecnológico de Monterrey.

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Pogorui, A.A., Rodríguez-Dagnino, R.M. Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations. J Stat Phys 145, 102 (2011). https://doi.org/10.1007/s10955-011-0328-2

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  • DOI: https://doi.org/10.1007/s10955-011-0328-2

Keywords

  • Random evolutions
  • Semi-Markov processes
  • Erlang distributions