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

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

doi:10.28924/2291-8639-22-2024-137

Research Article

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

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

* Corresponding author

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.

How to Cite

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

BibTeX

@article{Swarnambigai2024,
  author  = {Swarnambigai, P. and Nathiya, N. and Kalaivani, K. and Abodayeh, Kamaleldin},
  title   = {Classification of Random Walks and Green’s Theorem on Infinite Homogeneous Trees},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {137},
  doi     = {10.28924/2291-8639-22-2024-137}
}

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