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

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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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Authors and Affiliations

  1. Department of Mathematics, Zhytomyr State University, Valyka Berdychivska St., 40, 10008, Zhytomyr, Ukraine

    Anatoliy A. Pogorui

  2. Electrical and Computer Engineering, Tecnológico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, C.P. 64849, Monterrey, N.L., Mexico

    Ramón M. Rodríguez-Dagnino

Authors
  1. Anatoliy A. Pogorui
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  2. Ramón M. Rodríguez-Dagnino
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Corresponding author

Correspondence to Ramón M. Rodríguez-Dagnino.

Additional information

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

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