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Two-Dimensional Moran Model: Final Altitude and Number of Resets

Author

Listed:
  • Rafik Aguech

    (Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia)

  • Mohamed Abdelkader

    (Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude Z n . Finally, we analyse the statistical properties of N n X , the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function.

Suggested Citation

  • Rafik Aguech & Mohamed Abdelkader, 2023. "Two-Dimensional Moran Model: Final Altitude and Number of Resets," Mathematics, MDPI, vol. 11(17), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3774-:d:1231715
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    References listed on IDEAS

    as
    1. Itoh, Yoshiaki & Mahmoud, Hosam M., 2005. "Age statistics in the Moran population model," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 21-30, August.
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