Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb R$-trees

Asuman G. Aksoy; Monariah Al-Ansari; Qidi Peng

Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb R$-trees

Metric Geometry 2018-03-29 v2

Authors: Asuman G. Aksoy , Monariah Al-Ansari , Qidi Peng

Abstract

We provide a new representation of an $\mathbb R$ -tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the $\mathbb R$ -trees with radial and river metrics, and these sets of metric rays. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by $\mathbb R$ -trees.

Keywords

R-trees metric rays four-point condition radial metric river metric Brownian motion stochastic analysis representation theorems

Cite

@article{arxiv.1601.03108,
  title  = {Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb R$-trees},
  author = {Asuman G. Aksoy and Monariah Al-Ansari and Qidi Peng},
  journal= {arXiv preprint arXiv:1601.03108},
  year   = {2018}
}

Comments

17 pages, 805C05, 05C62, 60J65, 54E35 figures

Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb R$-trees

Abstract

Keywords

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