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Flying randomly in Rd with Dirichlet displacements

Author

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  • De Gregorio, Alessandro
  • Orsingher, Enzo

Abstract

Random flights in Rd,d≥2, with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position X¯d(t),t>0, when the number of changes of direction is fixed are obtained. The probability distributions are derived by inverting the characteristic functions for all dimensions d of Rd and many properties of the probabilistic structure of X¯d(t),t>0 are examined.

Suggested Citation

  • De Gregorio, Alessandro & Orsingher, Enzo, 2012. "Flying randomly in Rd with Dirichlet displacements," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 676-713.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:676-713
    DOI: 10.1016/j.spa.2011.10.009
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    Citations

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    Cited by:

    1. De Gregorio, Alessandro, 2017. "A note on isotropic random flights moving in mixed Poisson environments," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 311-317.
    2. De Gregorio, Alessandro, 2016. "Transport processes with random jump rate," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 127-134.
    3. Cinque, Fabrizio & Orsingher, Enzo, 2021. "On the exact distributions of the maximum of the asymmetric telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 601-633.
    4. Pogorui, Anatoliy A. & Rodríguez-Dagnino, Ramón M., 2019. "Goldstein-Kac telegraph equations and random flights in higher dimensions," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 617-629.
    5. Pogorui, Anatoliy A. & Rodríguez-Dagnino, Ramón M., 2013. "Random motion with gamma steps in higher dimensions," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1638-1643.
    6. Le Caër, Gérard, 2015. "Two-step Dirichlet random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 201-215.

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