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Flying randomly in Rd with Dirichlet displacements


  • De Gregorio, Alessandro
  • Orsingher, Enzo


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/

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    References listed on IDEAS

    1. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    2. Gilles Pag`es & Fabien Panloup, 2007. "Approximation of the distribution of a stationary Markov process with application to option pricing," Papers 0704.0335,, revised Sep 2009.
    3. Crauel, Hans, 1993. "Non-Markovian invariant measures are hyperbolic," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 13-28, March.
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    Cited by:

    1. repec:eee:stapro:v:129:y:2017:i:c:p:311-317 is not listed on IDEAS
    2. De Gregorio, Alessandro, 2016. "Transport processes with random jump rate," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 127-134.
    3. 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.
    4. 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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