Classification of Random Walks and Green’s Theorem on Infinite Homogeneous Trees

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DOI: https://doi.org/10.28924/2291-8639-22-2024-137
Published: Aug 15, 2024
Cite as:
P. Swarnambigai, N. Nathiya, K. Kalaivani, Kamaleldin Abodayeh, Classification of Random Walks and Green’s Theorem on Infinite Homogeneous Trees, Int. J. Anal. Appl., 22 (2024), 137.

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P. Swarnambigai, N. Nathiya, K. Kalaivani, Kamaleldin Abodayeh

Abstract

In the context of random walks whose states are the vertices of an infinite tree, a classification of random walks is given as transient or recurrent. On the infinite homogeneous trees with the assumption that the transition probability between any two neighboring states are the same, a form of the classical Green’s formula is derived. As a consequence, two versions of the mean-value property for median functions are obtained.

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