Axioms, Vol. 14, Pages 756: Non-Uniformly Multidimensional Moran Random Walk with Resets

Axioms doi: 10.3390/axioms14100756

Authors:
Mohamed Abdelkader

In this paper, we investigate the non-uniform m-dimensional Moran walk (Zn(1),…,Zn(m)), where each component process (Zn(j))1≤j≤m, either increases by one unit or resets to zero at each step. Using probability generating functions, we analyze key statistical properties of the walk, with particular emphasis on the mean and variance of its final altitude. We further establish closed-form expressions for the limiting distribution of the process, as well as for the mean and variance of each component. These results extend classical findings on one- and two-dimensional Moran models to the general m-dimensional setting, thereby providing new insights into the asymptotic behavior of multi-component random walks with resets.

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Mohamed Abdelkader www.mdpi.com