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

Rafik Aguech () and Mohamed Abdelkader ()
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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

Mathematics, 2023, vol. 11, issue 17, 1-22

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.

Keywords: random structure; random walk; probability generating function; height (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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