Skip to main content
SpringerLink
Log in

Multidimensional random motion with uniformly distributed changes of direction and erlang steps

  • Published:
Ukrainian Mathematical Journal Aims and scope

We study transport processes in ℝn, n ≥ 1; that have nonexponentially distributed sojourn times or non-Markovian step durations. We use the idea that the probabilistic properties of a random vector are completely determined by those of its projection to a fixed line, and, using this idea, we avoid many difficulties appearing in the analysis of these problems in higher dimensions. As a particular case, we find the probability density function in three dimensions for 2-Erlang-distributed sojourn times.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Di Crescenzo, “On random motions with velocities alternating at Erlang-distributed random times,” Adv. Appl. Probab., 61, 690–701 (2001).

    Google Scholar 

  2. A. A. Pogorui and R. M. Rodríguez-Dagnino, “One-dimensional semi-Markov evolutions with general Erlang sojourn times,” Rand. Oper. Stochast. Equat., 13, 1720–1724 (2005).

    Google Scholar 

  3. M. Pinsky, “Isotropic transport process on a Riemann manifold,” Trans. Amer. Math. Soc., 218, 353–360 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  4. E. Orsingher and A. De Gregorio, “Random flights in higher spaces,” J. Theor. Probab., 20, 769–806 (2007).

    Article  MATH  Google Scholar 

  5. A. D. Kolesnik, “Random motions at finite speed in higher dimensions,” J. Statist. Phys., 131, 1039–1065 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Stadje, “Exact solution for non-correlated random walk models,” J. Statist. Phys., 56, 415–435 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Le Caër, “A Pearson–Dirichlet random walk,” J. Statist. Phys., 40, 728–751 (2010).

    Article  Google Scholar 

  8. A. A. Pohorui, “Fading evolutions in multidimensional spaces,” Ukr. Mat. Zh., 62, No. 11, 1577–1582 (2010); English translation: Ukr. Math. J., 62, No. 11, 1828–1834 (2011).

    Google Scholar 

  9. V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific (2005).

  10. S. Bochner and K. Chandrasekharan, “Fourier transforms,” Ann. Math. Stud., No. 19 (1949).

Download references

Author information

Authors and Affiliations

  1. Zhytomyr State University, Zhytomyr, Ukraine

    A. A. Pogorui

  2. Monterrey Institute of Technology and Higher Education, Monterrey, Mexico

    R. M. Rodríguez-Dagnino

Authors
  1. A. A. Pogorui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. M. Rodríguez-Dagnino
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 572–576, April, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pogorui, A.A., Rodríguez-Dagnino, R.M. Multidimensional random motion with uniformly distributed changes of direction and erlang steps. Ukr Math J 63, 665–671 (2011). https://doi.org/10.1007/s11253-011-0533-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0533-9

Keywords

Search

Navigation